LMFDB - Embedded newform 4.37.b.b.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,37,Mod(3,4)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 37, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 37);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 37 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.8365034637$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + \cdots + 51\!\cdots\!00 $ x^16 + 6516989503065492x^14 + 17034486537407810917043361888198x^12 + 23072686962604400610679579162976738904788666844x^10 + 17414437736843557770548667414205720006669176493316634162548145x^8 + 7290100998556943999917076003638299976059510807819390063090897454035549344520x^6 + 1580065913442518903241377790659954072974637079040446265806555551201513339370568669874480400x^4 + 153535410141602761164144701301723551659810917407928334524859080419500779864196136193775339243188420422400*x^2 + 5156239739885100544994334306227490882529912274563409421561999152540966086224689966448180302613961864037075159771136000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.15
Root			$-1.85096e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.37.b.b.3.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(261200. - 22229.7i) q^{2} -2.96154e8i q^{3} +(6.77312e10 - 1.16128e10i) q^{4} +1.46296e12 q^{5} +(-6.58343e12 - 7.73554e13i) q^{6} +2.38729e15i q^{7} +(1.74332e16 - 4.53891e15i) q^{8} +6.23874e16 q^{9} +O(q^{10})$	\(q+(261200. - 22229.7i) q^{2} -2.96154e8i q^{3} +(6.77312e10 - 1.16128e10i) q^{4} +1.46296e12 q^{5} +(-6.58343e12 - 7.73554e13i) q^{6} +2.38729e15i q^{7} +(1.74332e16 - 4.53891e15i) q^{8} +6.23874e16 q^{9} +(3.82125e17 - 3.25212e16i) q^{10} +1.01014e19i q^{11} +(-3.43918e18 - 2.00589e19i) q^{12} -4.81295e19 q^{13} +(5.30689e19 + 6.23561e20i) q^{14} -4.33261e20i q^{15} +(4.45265e21 - 1.57310e21i) q^{16} +1.19657e22 q^{17} +(1.62956e22 - 1.38686e21i) q^{18} +1.66265e22i q^{19} +(9.90879e22 - 1.69891e22i) q^{20} +7.07007e23 q^{21} +(2.24553e23 + 2.63850e24i) q^{22} -2.63389e24i q^{23} +(-1.34422e24 - 5.16292e24i) q^{24} -1.24117e25 q^{25} +(-1.25714e25 + 1.06991e24i) q^{26} -6.29274e25i q^{27} +(2.77232e25 + 1.61694e26i) q^{28} +1.36780e26 q^{29} +(-9.63129e24 - 1.13168e26i) q^{30} +4.52800e26i q^{31} +(1.12806e27 - 5.09874e26i) q^{32} +2.99159e27 q^{33} +(3.12544e27 - 2.65994e26i) q^{34} +3.49251e27i q^{35} +(4.22557e27 - 7.24493e26i) q^{36} +5.31006e27 q^{37} +(3.69602e26 + 4.34283e27i) q^{38} +1.42538e28i q^{39} +(2.55041e28 - 6.64024e27i) q^{40} +1.73682e29 q^{41} +(1.84670e29 - 1.57166e28i) q^{42} -2.26096e29i q^{43} +(1.17306e29 + 6.84183e29i) q^{44} +9.12702e28 q^{45} +(-5.85506e28 - 6.87970e29i) q^{46} +1.08183e30i q^{47} +(-4.65879e29 - 1.31867e30i) q^{48} -3.04744e30 q^{49} +(-3.24192e30 + 2.75908e29i) q^{50} -3.54369e30i q^{51} +(-3.25987e30 + 5.58919e29i) q^{52} -1.23762e31 q^{53} +(-1.39886e30 - 1.64366e31i) q^{54} +1.47780e31i q^{55} +(1.08357e31 + 4.16182e31i) q^{56} +4.92399e30 q^{57} +(3.57270e31 - 3.04059e30i) q^{58} -9.54768e31i q^{59} +(-5.03138e30 - 2.93453e31i) q^{60} -5.38786e31 q^{61} +(1.00656e31 + 1.18271e32i) q^{62} +1.48937e32i q^{63} +(2.83315e32 - 1.58255e32i) q^{64} -7.04115e31 q^{65} +(7.81401e32 - 6.65022e31i) q^{66} +6.26685e32i q^{67} +(8.10450e32 - 1.38955e32i) q^{68} -7.80036e32 q^{69} +(7.76377e31 + 9.12244e32i) q^{70} -2.83770e33i q^{71} +(1.08761e33 - 2.83171e32i) q^{72} -6.34742e33 q^{73} +(1.38699e33 - 1.18041e32i) q^{74} +3.67577e33i q^{75} +(1.93080e32 + 1.12613e33i) q^{76} -2.41151e34 q^{77} +(3.16857e32 + 3.72308e33i) q^{78} -2.21307e34i q^{79} +(6.51405e33 - 2.30138e33i) q^{80} -9.27220e33 q^{81} +(4.53656e34 - 3.86089e33i) q^{82} +6.15416e34i q^{83} +(4.78864e34 - 8.21033e33i) q^{84} +1.75053e34 q^{85} +(-5.02606e33 - 5.90563e34i) q^{86} -4.05081e34i q^{87} +(4.58495e34 + 1.76101e35i) q^{88} -8.78919e34 q^{89} +(2.38398e34 - 2.02891e33i) q^{90} -1.14899e35i q^{91} +(-3.05868e34 - 1.78396e35i) q^{92} +1.34099e35 q^{93} +(2.40488e34 + 2.82573e35i) q^{94} +2.43238e34i q^{95} +(-1.51001e35 - 3.34080e35i) q^{96} +1.81673e35 q^{97} +(-7.95991e35 + 6.77438e34i) q^{98} +6.30203e35i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots - 93\!\cdots\!68 q^{9}+O(q^{10}) $ 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9	$ 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots + 10\!\cdots\!28 q^{98}+O(q^{100}) $ 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9 - 2378142919315561000 * q^10 - 42882825786868930560 * q^12 + 194612014165659174176 * q^13 + 360192888461659120128 * q^14 - 22854023522524990832384 * q^16 + 41803218917907805318176 * q^17 + 138204474036544564333068 * q^18 + 104592026972614096023840 * q^20 - 175281296641396774711296 * q^21 - 4320007363229839528400640 * q^22 + 5118364442017682383085568 * q^24 + 61061610541832160307690800 * q^25 - 70158486911796111631798440 * q^26 - 303534200373547502486016000 * q^28 - 95320519344473743554877152 * q^29 + 361206724962468787334008320 * q^30 + 4662427702586163916855016448 * q^32 - 877278707167997370072668160 * q^33 - 9018225886246079564307746920 * q^34 - 927455191590908629268766192 * q^36 - 30841755082751179145922114784 * q^37 + 78752216997100984306444174080 * q^38 - 138122339194153338361474460800 * q^40 + 99165040763128472781035553312 * q^41 - 193406458925326074258433843200 * q^42 + 303084904999663560614745692160 * q^44 + 1511424637230487714612565241120 * q^45 - 919681205391808405630032112128 * q^46 - 1511312501851283767715389931520 * q^48 - 11342315683204385026834539108848 * q^49 + 11057816114707215621338245966500 * q^50 + 16094442403868561017575461524256 * q^52 + 20911545776251998404629518049056 * q^53 - 42689634574575573966970327785984 * q^54 - 18346492780981997297263940026368 * q^56 - 17591710635767034592583231047680 * q^57 + 33019206317228013320629044602456 * q^58 - 69704584574466315130190074982400 * q^60 + 216576725773383276684585233875232 * q^61 + 406820870675021165265665434183680 * q^62 - 266111502464782094817164314013696 * q^64 - 2065823886943449026422930314993600 * q^65 - 816784109200805225218136599695360 * q^66 + 3502994508232801473127246422490656 * q^68 + 3923547517779842564469076002041856 * q^69 + 312094823977274793710809307489280 * q^70 - 1875458138040165128132392402132032 * q^72 - 13529699358917711874787838251408864 * q^73 + 7683713356825244783786618034273240 * q^74 - 15736875982808342938482824299100160 * q^76 + 22639774155764461736245527294259200 * q^77 - 18389491597233550087389536189698560 * q^78 + 67235988583903584940074904608207360 * q^80 - 40716877106976112078739817594850800 * q^81 + 43227843112149006015980010857549336 * q^82 - 37119022564017857733030089777086464 * q^84 - 206886985961236391219562146270052800 * q^85 + 102108696026625816655543232864792832 * q^86 + 39749581676781586144951142033940480 * q^88 + 461506837768868190077604450557625888 * q^89 - 361659211507857840778210819426233000 * q^90 - 17511543929609412714530045318983680 * q^92 - 231978818535002459544922699145134080 * q^93 - 696830931593880576023589572144120832 * q^94 + 1050073689946737522972596709346639872 * q^96 + 451372245708940284684446048339288096 * q^97 + 1035415270688230597220229005750452428 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	261200.	−	22229.7i	0.996398	−	0.0847997i
$2$	261200.	−	22229.7i	0.996398	−	0.0847997i
$3$		−	2.96154e8i		−	0.764425i	−0.924074	−	0.382213i	$-0.875162\pi$
$3$		−	2.96154e8i		−	0.764425i	0.924074	−	0.382213i	$-0.124838\pi$
$4$	6.77312e10	−	1.16128e10i	0.985618	−	0.168989i
$5$	1.46296e12			0.383506			0.191753	−	0.981443i	$-0.438583\pi$
$5$	1.46296e12			0.383506			0.191753	+	0.981443i	$0.438583\pi$
$6$	−6.58343e12	−	7.73554e13i	−0.0648231	−	0.761672i
$7$			2.38729e15i			1.46602i	0.680216	+	0.733012i	$0.261886\pi$
$7$			2.38729e15i			1.46602i	−0.680216	+	0.733012i	$0.738114\pi$
$8$	1.74332e16	−	4.53891e15i	0.967738	−	0.251960i
$9$	6.23874e16			0.415654
$10$	3.82125e17	−	3.25212e16i	0.382125	−	0.0325212i
$11$			1.01014e19i			1.81683i	0.418065	+	0.908417i	$0.362708\pi$
$11$			1.01014e19i			1.81683i	−0.418065	+	0.908417i	$0.637292\pi$
$12$	−3.43918e18	−	2.00589e19i	−0.129179	−	0.753432i
$13$	−4.81295e19			−0.427988			−0.213994	−	0.976835i	$-0.568647\pi$
$13$	−4.81295e19			−0.427988			−0.213994	+	0.976835i	$0.568647\pi$
$14$	5.30689e19	+	6.23561e20i	0.124318	+	1.46074i
$15$		−	4.33261e20i		−	0.293162i
$16$	4.45265e21	−	1.57310e21i	0.942886	−	0.333116i
$17$	1.19657e22			0.850858			0.425429	−	0.904992i	$-0.360123\pi$
$17$	1.19657e22			0.850858			0.425429	+	0.904992i	$0.360123\pi$
$18$	1.62956e22	−	1.38686e21i	0.414156	−	0.0352473i
$19$			1.66265e22i			0.159674i	0.996808	+	0.0798371i	$0.0254400\pi$
$19$			1.66265e22i			0.159674i	−0.996808	+	0.0798371i	$0.974560\pi$
$20$	9.90879e22	−	1.69891e22i	0.377990	−	0.0648081i
$21$	7.07007e23			1.12067
$22$	2.24553e23	+	2.63850e24i	0.154067	+	1.81029i
$23$		−	2.63389e24i		−	0.811888i	−0.913898	−	0.405944i	$-0.866943\pi$
$23$		−	2.63389e24i		−	0.811888i	0.913898	−	0.405944i	$-0.133057\pi$
$24$	−1.34422e24	−	5.16292e24i	−0.192605	−	0.739763i
$25$	−1.24117e25			−0.852923
$26$	−1.25714e25	+	1.06991e24i	−0.426446	+	0.0362932i
$27$		−	6.29274e25i		−	1.08216i
$28$	2.77232e25	+	1.61694e26i	0.247741	+	1.44494i
$29$	1.36780e26			0.649920			0.324960	−	0.945728i	$-0.394649\pi$
$29$	1.36780e26			0.649920			0.324960	+	0.945728i	$0.394649\pi$
$30$	−9.63129e24	−	1.13168e26i	−0.0248600	−	0.292106i
$31$			4.52800e26i			0.647733i	0.946103	+	0.323866i	$0.104983\pi$
$31$			4.52800e26i			0.647733i	−0.946103	+	0.323866i	$0.895017\pi$
$32$	1.12806e27	−	5.09874e26i	0.911241	−	0.411873i
$33$	2.99159e27			1.38883
$34$	3.12544e27	−	2.65994e26i	0.847793	−	0.0721525i
$35$			3.49251e27i			0.562229i
$36$	4.22557e27	−	7.24493e26i	0.409676	−	0.0702407i
$37$	5.31006e27			0.314390			0.157195	−	0.987568i	$-0.449755\pi$
$37$	5.31006e27			0.314390			0.157195	+	0.987568i	$0.449755\pi$
$38$	3.69602e26	+	4.34283e27i	0.0135403	+	0.159099i
$39$			1.42538e28i			0.327165i
$40$	2.55041e28	−	6.64024e27i	0.371133	−	0.0966282i
$41$	1.73682e29			1.62048			0.810241	−	0.586097i	$-0.199336\pi$
$41$	1.73682e29			1.62048			0.810241	+	0.586097i	$0.199336\pi$
$42$	1.84670e29	−	1.57166e28i	1.11663	−	0.0950322i
$43$		−	2.26096e29i		−	0.895079i	−0.894264	−	0.447539i	$-0.852300\pi$
$43$		−	2.26096e29i		−	0.895079i	0.894264	−	0.447539i	$-0.147700\pi$
$44$	1.17306e29	+	6.84183e29i	0.307024	+	1.79070i
$45$	9.12702e28			0.159406
$46$	−5.85506e28	−	6.87970e29i	−0.0688478	−	0.808963i
$47$			1.08183e30i			0.863768i	0.901929	+	0.431884i	$0.142151\pi$
$47$			1.08183e30i			0.863768i	−0.901929	+	0.431884i	$0.857849\pi$
$48$	−4.65879e29	−	1.31867e30i	−0.254643	−	0.720766i
$49$	−3.04744e30			−1.14923
$50$	−3.24192e30	+	2.75908e29i	−0.849851	+	0.0723277i
$51$		−	3.54369e30i		−	0.650418i
$52$	−3.25987e30	+	5.58919e29i	−0.421832	+	0.0723250i
$53$	−1.23762e31			−1.13664			−0.568319	−	0.822808i	$-0.692406\pi$
$53$	−1.23762e31			−1.13664			−0.568319	+	0.822808i	$0.692406\pi$
$54$	−1.39886e30	−	1.64366e31i	−0.0917670	−	1.07826i
$55$			1.47780e31i			0.696767i
$56$	1.08357e31	+	4.16182e31i	0.369379	+	1.41873i
$57$	4.92399e30			0.122059
$58$	3.57270e31	−	3.04059e30i	0.647579	−	0.0551131i
$59$		−	9.54768e31i		−	1.27222i	−0.771599	−	0.636109i	$-0.780543\pi$
$59$		−	9.54768e31i		−	1.27222i	0.771599	−	0.636109i	$-0.219457\pi$
$60$	−5.03138e30	−	2.93453e31i	−0.0495410	−	0.288945i
$61$	−5.38786e31			−0.393985			−0.196992	−	0.980405i	$-0.563117\pi$
$61$	−5.38786e31			−0.393985			−0.196992	+	0.980405i	$0.563117\pi$
$62$	1.00656e31	+	1.18271e32i	0.0549276	+	0.645400i
$63$			1.48937e32i			0.609358i
$64$	2.83315e32	−	1.58255e32i	0.873032	−	0.487662i
$65$	−7.04115e31			−0.164136
$66$	7.81401e32	−	6.65022e31i	1.38383	−	0.117773i
$67$			6.26685e32i			0.846647i	0.905979	+	0.423324i	$0.139137\pi$
$67$			6.26685e32i			0.846647i	−0.905979	+	0.423324i	$0.860863\pi$
$68$	8.10450e32	−	1.38955e32i	0.838621	−	0.143785i
$69$	−7.80036e32			−0.620628
$70$	7.76377e31	+	9.12244e32i	0.0476769	+	0.560204i
$71$		−	2.83770e33i		−	1.34994i	−0.737843	−	0.674972i	$-0.764156\pi$
$71$		−	2.83770e33i		−	1.34994i	0.737843	−	0.674972i	$-0.235844\pi$
$72$	1.08761e33	−	2.83171e32i	0.402244	−	0.104728i
$73$	−6.34742e33			−1.83141			−0.915705	−	0.401851i	$-0.868367\pi$
$73$	−6.34742e33			−1.83141			−0.915705	+	0.401851i	$0.868367\pi$
$74$	1.38699e33	−	1.18041e32i	0.313258	−	0.0266602i
$75$			3.67577e33i			0.651996i
$76$	1.93080e32	+	1.12613e33i	0.0269831	+	0.157378i
$77$	−2.41151e34			−2.66352
$78$	3.16857e32	+	3.72308e33i	0.0277435	+	0.325986i
$79$		−	2.21307e34i		−	1.54066i	−0.637645	−	0.770330i	$-0.720091\pi$
$79$		−	2.21307e34i		−	1.54066i	0.637645	−	0.770330i	$-0.279909\pi$
$80$	6.51405e33	−	2.30138e33i	0.361602	−	0.127752i
$81$	−9.27220e33			−0.411578
$82$	4.53656e34	−	3.86089e33i	1.61464	−	0.137416i
$83$			6.15416e34i			1.76102i	0.474031	+	0.880508i	$0.342799\pi$
$83$			6.15416e34i			1.76102i	−0.474031	+	0.880508i	$0.657201\pi$
$84$	4.78864e34	−	8.21033e33i	1.10455	−	0.189380i
$85$	1.75053e34			0.326309
$86$	−5.02606e33	−	5.90563e34i	−0.0759024	−	0.891855i
$87$		−	4.05081e34i		−	0.496816i
$88$	4.58495e34	+	1.76101e35i	0.457770	+	1.75822i
$89$	−8.78919e34			−0.716026			−0.358013	−	0.933717i	$-0.616546\pi$
$89$	−8.78919e34			−0.716026			−0.358013	+	0.933717i	$0.616546\pi$
$90$	2.38398e34	−	2.02891e33i	0.158831	−	0.0135176i
$91$		−	1.14899e35i		−	0.627440i
$92$	−3.05868e34	−	1.78396e35i	−0.137200	−	0.800211i
$93$	1.34099e35			0.495144
$94$	2.40488e34	+	2.82573e35i	0.0732473	+	0.860657i
$95$			2.43238e34i			0.0612360i
$96$	−1.51001e35	−	3.34080e35i	−0.314846	−	0.696576i
$97$	1.81673e35			0.314340			0.157170	−	0.987572i	$-0.449763\pi$
$97$	1.81673e35			0.314340			0.157170	+	0.987572i	$0.449763\pi$
$98$	−7.95991e35	+	6.77438e34i	−1.14509	+	0.0974541i
$99$			6.30203e35i			0.755174i
$100$	−8.40656e35	+	1.44134e35i	−0.840656	+	0.144134i
$101$	5.19200e35			0.434060			0.217030	−	0.976165i	$-0.430363\pi$
$101$	5.19200e35			0.434060			0.217030	+	0.976165i	$0.430363\pi$
$102$	−7.87753e34	−	9.25611e35i	−0.0551552	−	0.648075i
$103$		−	7.57511e35i		−	0.444958i	−0.974937	−	0.222479i	$-0.928585\pi$
$103$		−	7.57511e35i		−	0.444958i	0.974937	−	0.222479i	$-0.0714149\pi$
$104$	−8.39052e35	+	2.18455e35i	−0.414180	+	0.107836i
$105$	1.03432e36			0.429782
$106$	−3.23266e36	+	2.75120e35i	−1.13254	+	0.0963866i
$107$			1.18309e36i			0.350034i	0.984565	+	0.175017i	$0.0559980\pi$
$107$			1.18309e36i			0.350034i	−0.984565	+	0.175017i	$0.944002\pi$
$108$	−7.30764e35	−	4.26215e36i	−0.182873	−	1.06660i
$109$	5.99820e36			1.27158			0.635791	−	0.771861i	$-0.280674\pi$
$109$	5.99820e36			1.27158			0.635791	+	0.771861i	$0.280674\pi$
$110$	3.28511e35	+	3.86001e36i	0.0590856	+	0.694257i
$111$		−	1.57260e36i		−	0.240328i
$112$	3.75545e36	+	1.06298e37i	0.488357	+	1.38229i
$113$	1.38128e37			1.53063			0.765314	−	0.643657i	$-0.222584\pi$
$113$	1.38128e37			1.53063			0.765314	+	0.643657i	$0.222584\pi$
$114$	1.28615e36	−	1.09459e35i	0.121619	−	0.0103506i
$115$		−	3.85327e36i		−	0.311364i
$116$	9.26430e36	−	1.58840e36i	0.640573	−	0.109829i
$117$	−3.00268e36			−0.177895
$118$	−2.12242e36	−	2.49385e37i	−0.107884	−	1.26764i
$119$			2.85656e37i			1.24738i
$120$	−1.96653e36	−	7.55314e36i	−0.0738650	−	0.283704i
$121$	−7.11266e37			−2.30089
$122$	−1.40731e37	+	1.19771e36i	−0.392566	+	0.0334098i
$123$		−	5.14365e37i		−	1.23874i
$124$	5.25828e36	+	3.06687e37i	0.109459	+	0.638417i
$125$	−3.94466e37			−0.710607
$126$	3.31083e36	+	3.89023e37i	0.0516734	+	0.607163i
$127$			3.83191e37i			0.518739i	0.965778	+	0.259369i	$0.0835147\pi$
$127$			3.83191e37i			0.518739i	−0.965778	+	0.259369i	$0.916485\pi$
$128$	7.04839e37	−	4.76343e37i	0.828534	−	0.559939i
$129$	−6.69594e37			−0.684221
$130$	−1.83915e37	+	1.56523e36i	−0.163545	+	0.0139187i
$131$		−	7.43704e37i		−	0.576125i	−0.957612	−	0.288062i	$-0.906989\pi$
$131$		−	7.43704e37i		−	0.576125i	0.957612	−	0.288062i	$-0.0930111\pi$
$132$	2.02624e38	−	3.47407e37i	1.36886	−	0.234697i
$133$	−3.96922e37			−0.234086
$134$	1.39310e37	+	1.63690e38i	0.0717955	+	0.843598i
$135$		−	9.20602e37i		−	0.415015i
$136$	2.08600e38	−	5.43112e37i	0.823408	−	0.214382i
$137$	6.29514e37			0.217788			0.108894	−	0.994053i	$-0.465269\pi$
$137$	6.29514e37			0.217788			0.108894	+	0.994053i	$0.465269\pi$
$138$	−2.03745e38	+	1.73400e37i	−0.618392	+	0.0526291i
$139$			5.21959e38i			1.39114i	0.718459	+	0.695569i	$0.244848\pi$
$139$			5.21959e38i			1.39114i	−0.718459	+	0.695569i	$0.755152\pi$
$140$	4.05579e37	+	2.36552e38i	0.0950103	+	0.554143i
$141$	3.20388e38			0.660286
$142$	−6.30813e37	−	7.41206e38i	−0.114475	−	1.34508i
$143$		−	4.86178e38i		−	0.777583i
$144$	2.77789e38	−	9.81414e37i	0.391914	−	0.138461i
$145$	2.00104e38			0.249248
$146$	−1.65794e39	+	1.41101e38i	−1.82481	+	0.155303i
$147$			9.02512e38i			0.878498i
$148$	3.59657e38	−	6.16648e37i	0.309868	−	0.0531283i
$149$	1.11386e39			0.850113			0.425056	−	0.905167i	$-0.360254\pi$
$149$	1.11386e39			0.850113			0.425056	+	0.905167i	$0.360254\pi$
$150$	8.17113e37	+	9.60109e38i	0.0552891	+	0.649648i
$151$		−	2.20582e39i		−	1.32430i	−0.749372	−	0.662149i	$-0.769645\pi$
$151$		−	2.20582e39i		−	1.32430i	0.749372	−	0.662149i	$-0.230355\pi$
$152$	7.54660e37	+	2.89853e38i	0.0402315	+	0.154523i
$153$	7.46508e38			0.353662
$154$	−6.29886e39	+	5.36073e38i	−2.65393	+	0.225866i
$155$			6.62428e38i			0.248409i
$156$	1.65526e38	+	9.65423e38i	0.0552871	+	0.322459i
$157$	−2.97211e39			−0.884853			−0.442427	−	0.896805i	$-0.645882\pi$
$157$	−2.97211e39			−0.884853			−0.442427	+	0.896805i	$0.645882\pi$
$158$	−4.91959e38	−	5.78052e39i	−0.130648	−	1.53511i
$159$			3.66527e39i			0.868875i
$160$	1.65031e39	−	7.45925e38i	0.349466	−	0.157956i
$161$	6.28786e39			1.19025
$162$	−2.42190e39	+	2.06119e38i	−0.410096	+	0.0349017i
$163$		−	5.14197e39i		−	0.779386i	−0.920945	−	0.389693i	$-0.872581\pi$
$163$		−	5.14197e39i		−	0.779386i	0.920945	−	0.389693i	$-0.127419\pi$
$164$	1.17636e40	−	2.01693e39i	1.59718	−	0.273843i
$165$	4.37657e39			0.532626
$166$	1.36805e39	+	1.60747e40i	0.149334	+	1.75467i
$167$			8.78588e39i			0.860773i	0.902645	+	0.430387i	$0.141623\pi$
$167$			8.78588e39i			0.860773i	−0.902645	+	0.430387i	$0.858377\pi$
$168$	1.23254e40	−	3.20904e39i	1.08451	−	0.282363i
$169$	−1.03298e40			−0.816827
$170$	4.57238e39	−	3.89139e38i	0.325134	−	0.0276709i
$171$			1.03728e39i			0.0663692i
$172$	−2.62561e39	−	1.53138e40i	−0.151258	−	0.882206i
$173$	−1.25353e40			−0.650585			−0.325292	−	0.945613i	$-0.605463\pi$
$173$	−1.25353e40			−0.650585			−0.325292	+	0.945613i	$0.605463\pi$
$174$	−9.00484e38	−	1.05807e40i	−0.0421298	−	0.495026i
$175$		−	2.96303e40i		−	1.25041i
$176$	1.58906e40	+	4.49782e40i	0.605217	+	1.71307i
$177$	−2.82758e40			−0.972516
$178$	−2.29573e40	+	1.95381e39i	−0.713447	+	0.0607188i
$179$		−	4.92645e39i		−	0.138414i	−0.997602	−	0.0692070i	$-0.977953\pi$
$179$		−	4.92645e39i		−	0.138414i	0.997602	−	0.0692070i	$-0.0220469\pi$
$180$	6.18184e39	−	1.05990e39i	0.157113	−	0.0269377i
$181$	−7.14294e40			−1.64310			−0.821548	−	0.570140i	$-0.806889\pi$
$181$	−7.14294e40			−1.64310			−0.821548	+	0.570140i	$0.806889\pi$
$182$	−2.55418e39	−	3.00117e40i	−0.0532068	−	0.625180i
$183$			1.59564e40i			0.301172i
$184$	−1.19550e40	−	4.59171e40i	−0.204563	−	0.785694i
$185$	7.76841e39			0.120570
$186$	3.50265e40	−	2.98098e39i	0.493360	−	0.0419880i
$187$			1.20871e41i			1.54587i
$188$	1.25631e40	+	7.32735e40i	0.145967	+	0.851345i
$189$	1.50226e41			1.58648
$190$	5.40712e38	+	6.35338e39i	0.00519280	+	0.0610155i
$191$		−	1.55729e41i		−	1.36072i	−0.732876	−	0.680362i	$-0.761822\pi$
$191$		−	1.55729e41i		−	1.36072i	0.732876	−	0.680362i	$-0.238178\pi$
$192$	−4.68680e40	−	8.39050e40i	−0.372782	−	0.667368i
$193$	9.98102e40			0.723008			0.361504	−	0.932371i	$-0.382263\pi$
$193$	9.98102e40			0.723008			0.361504	+	0.932371i	$0.382263\pi$
$194$	4.74531e40	−	4.03855e39i	0.313208	−	0.0266560i
$195$			2.08527e40i			0.125470i
$196$	−2.06407e41	+	3.53893e40i	−1.13270	+	0.194206i
$197$	1.02224e41			0.511871			0.255935	−	0.966694i	$-0.417617\pi$
$197$	1.02224e41			0.511871			0.255935	+	0.966694i	$0.417617\pi$
$198$	1.40092e40	+	1.64609e41i	0.0640385	+	0.752454i
$199$		−	8.08444e40i		−	0.337516i	−0.985657	−	0.168758i	$-0.946024\pi$
$199$		−	8.08444e40i		−	0.337516i	0.985657	−	0.168758i	$-0.0539757\pi$
$200$	−2.16375e41	+	5.63354e40i	−0.825406	+	0.214903i
$201$	1.85595e41			0.647199
$202$	1.35615e41	−	1.15417e40i	0.432497	−	0.0368082i
$203$			3.26535e41i			0.952799i
$204$	−4.11522e40	−	2.40018e41i	−0.109913	−	0.641063i
$205$	2.54089e41			0.621464
$206$	−1.68393e40	−	1.97862e41i	−0.0377323	−	0.443355i
$207$		−	1.64321e41i		−	0.337464i
$208$	−2.14304e41	+	7.57124e40i	−0.403543	+	0.142570i
$209$	−1.67951e41			−0.290102
$210$	2.70165e41	−	2.29927e40i	0.428234	−	0.0364454i
$211$		−	5.10879e40i		−	0.0743420i	−0.999309	−	0.0371710i	$-0.988165\pi$
$211$		−	5.10879e40i		−	0.0743420i	0.999309	−	0.0371710i	$-0.0118346\pi$
$212$	−8.38255e41	+	1.43723e41i	−1.12029	+	0.192079i
$213$	−8.40396e41			−1.03193
$214$	2.62998e40	+	3.09023e41i	0.0296828	+	0.348773i
$215$		−	3.30770e41i		−	0.343268i
$216$	−2.85622e41	−	1.09703e42i	−0.272661	−	1.04725i
$217$	−1.08097e42			−0.949592
$218$	1.56673e42	−	1.33339e41i	1.26700	−	0.107830i
$219$			1.87981e42i			1.39998i
$220$	1.71614e41	+	1.00093e42i	0.117746	+	0.686746i
$221$	−5.75903e41			−0.364157
$222$	−3.49584e40	−	4.10762e41i	−0.0203797	−	0.239462i
$223$		−	3.14384e42i		−	1.69033i	−0.534503	−	0.845167i	$-0.679501\pi$
$223$		−	3.14384e42i		−	1.69033i	0.534503	−	0.845167i	$-0.320499\pi$
$224$	1.21722e42	+	2.69302e42i	0.603816	+	1.33590i
$225$	−7.74331e41			−0.354521
$226$	3.60790e42	−	3.07055e41i	1.52512	−	0.129797i
$227$		−	2.54173e42i		−	0.992347i	−0.868223	−	0.496174i	$-0.834738\pi$
$227$		−	2.54173e42i		−	0.992347i	0.868223	−	0.496174i	$-0.165262\pi$
$228$	3.33508e41	−	5.71814e40i	0.120304	−	0.0206266i
$229$	3.08692e42			1.02917			0.514585	−	0.857440i	$-0.327946\pi$
$229$	3.08692e42			1.02917			0.514585	+	0.857440i	$0.327946\pi$
$230$	−8.56571e40	−	1.00647e42i	−0.0264036	−	0.310242i
$231$			7.14179e42i			2.03606i
$232$	2.38452e42	−	6.20834e41i	0.628952	−	0.163754i
$233$	7.31206e41			0.178498			0.0892489	−	0.996009i	$-0.471553\pi$
$233$	7.31206e41			0.178498			0.0892489	+	0.996009i	$0.471553\pi$
$234$	−7.84298e41	+	6.67487e40i	−0.177254	+	0.0150854i
$235$			1.58267e42i			0.331260i
$236$	−1.10875e42	−	6.46675e42i	−0.214990	−	1.25392i
$237$	−6.55409e42			−1.17772
$238$	6.35006e41	+	7.46133e42i	0.105777	+	1.24289i
$239$		−	3.35689e42i		−	0.518532i	−0.965806	−	0.259266i	$-0.916519\pi$
$239$		−	3.35689e42i		−	0.518532i	0.965806	−	0.259266i	$-0.0834806\pi$
$240$	−6.81562e41	−	1.92916e42i	−0.0976570	−	0.276418i
$241$	2.11826e42			0.281626			0.140813	−	0.990036i	$-0.455028\pi$
$241$	2.11826e42			0.281626			0.140813	+	0.990036i	$0.455028\pi$
$242$	−1.85782e43	+	1.58113e42i	−2.29260	+	0.195115i
$243$		−	6.69907e42i		−	0.767541i
$244$	−3.64926e42	+	6.25682e41i	−0.388319	+	0.0665789i
$245$	−4.45828e42			−0.440735
$246$	−1.14342e42	−	1.34352e43i	−0.105045	−	1.23428i
$247$		−	8.00224e41i		−	0.0683386i
$248$	2.05522e42	+	7.89376e42i	0.163203	+	0.626836i
$249$	1.82258e43			1.34617
$250$	−1.03034e43	+	8.76888e41i	−0.708047	+	0.0602593i
$251$			1.09661e43i			0.701336i	0.936500	+	0.350668i	$0.114045\pi$
$251$			1.09661e43i			0.701336i	−0.936500	+	0.350668i	$0.885955\pi$
$252$	1.72958e42	+	1.00877e43i	0.102975	+	0.600595i
$253$	2.66061e43			1.47507
$254$	8.51824e41	+	1.00089e43i	0.0439889	+	0.516870i
$255$		−	5.18427e42i		−	0.249439i
$256$	1.73515e43	−	1.40089e43i	0.778067	−	0.628181i
$257$	−5.04919e42			−0.211070			−0.105535	−	0.994416i	$-0.533655\pi$
$257$	−5.04919e42			−0.211070			−0.105535	+	0.994416i	$0.533655\pi$
$258$	−1.74898e43	+	1.48849e42i	−0.681757	+	0.0580218i
$259$			1.26767e43i			0.460903i
$260$	−4.76905e42	+	8.17675e41i	−0.161775	+	0.0277371i
$261$	8.53337e42			0.270142
$262$	−1.65323e42	−	1.94255e43i	−0.0488552	−	0.574050i
$263$		−	2.22021e43i		−	0.612620i	−0.951932	−	0.306310i	$-0.900906\pi$
$263$		−	2.22021e43i		−	0.612620i	0.951932	−	0.306310i	$-0.0990943\pi$
$264$	5.21529e43	−	1.35785e43i	1.34403	−	0.349931i
$265$	−1.81059e43			−0.435907
$266$	−1.03676e43	+	8.82348e41i	−0.233243	+	0.0198505i
$267$			2.60296e43i			0.547349i
$268$	7.27757e42	+	4.24461e43i	0.143074	+	0.834471i
$269$	−2.41057e43			−0.443178			−0.221589	−	0.975140i	$-0.571124\pi$
$269$	−2.41057e43			−0.443178			−0.221589	+	0.975140i	$0.571124\pi$
$270$	−2.04648e42	−	2.40461e43i	−0.0351932	−	0.413521i
$271$			4.83064e43i			0.777244i	0.921397	+	0.388622i	$0.127049\pi$
$271$			4.83064e43i			0.777244i	−0.921397	+	0.388622i	$0.872951\pi$
$272$	5.32791e43	−	1.88232e43i	0.802262	−	0.283435i
$273$	−3.40279e43			−0.479631
$274$	1.64429e43	−	1.39939e42i	0.217004	−	0.0184684i
$275$		−	1.25376e44i		−	1.54962i
$276$	−5.28327e43	+	9.05841e42i	−0.611702	+	0.104879i
$277$	−1.00881e44			−1.09439			−0.547196	−	0.837005i	$-0.684305\pi$
$277$	−1.00881e44			−1.09439			−0.547196	+	0.837005i	$0.684305\pi$
$278$	1.16030e43	+	1.36336e44i	0.117968	+	1.38613i
$279$			2.82490e43i			0.269233i
$280$	1.58522e43	+	6.08857e43i	0.141659	+	0.544090i
$281$	−1.08851e44			−0.912261			−0.456130	−	0.889913i	$-0.650765\pi$
$281$	−1.08851e44			−0.912261			−0.456130	+	0.889913i	$0.650765\pi$
$282$	8.36853e43	−	7.12214e42i	0.657908	−	0.0559921i
$283$		−	2.09138e44i		−	1.54268i	−0.636421	−	0.771342i	$-0.719586\pi$
$283$		−	2.09138e44i		−	1.54268i	0.636421	−	0.771342i	$-0.280414\pi$
$284$	−3.29536e43	−	1.92201e44i	−0.228125	−	1.33053i
$285$	7.20360e42			0.0468104
$286$	−1.08076e43	−	1.26990e44i	−0.0659388	−	0.774782i
$287$			4.14629e44i			2.37567i
$288$	7.03768e43	−	3.18097e43i	0.378761	−	0.171196i
$289$	−5.45926e43			−0.276040
$290$	5.22672e43	−	4.44826e42i	0.248350	−	0.0211362i
$291$		−	5.38033e43i		−	0.240290i
$292$	−4.29918e44	+	7.37113e43i	−1.80507	+	0.309487i
$293$	1.29240e44			0.510246			0.255123	−	0.966909i	$-0.417884\pi$
$293$	1.29240e44			0.510246			0.255123	+	0.966909i	$0.417884\pi$
$294$	2.00626e43	+	2.35736e44i	0.0744964	+	0.875334i
$295$		−	1.39679e44i		−	0.487903i
$296$	9.25715e43	−	2.41019e43i	0.304247	−	0.0792137i
$297$	6.35658e44			1.96611
$298$	2.90939e44	−	2.47607e43i	0.847051	−	0.0720893i
$299$			1.26768e44i			0.347478i
$300$	4.26860e43	+	2.48964e44i	0.110180	+	0.642619i
$301$	5.39758e44			1.31221
$302$	−4.90349e43	−	5.76160e44i	−0.112300	−	1.31953i
$303$		−	1.53763e44i		−	0.331807i
$304$	2.61550e43	+	7.40318e43i	0.0531901	+	0.150555i
$305$	−7.88222e43			−0.151096
$306$	1.94988e44	−	1.65947e43i	0.352388	−	0.0299905i
$307$			5.37830e44i			0.916546i	0.888812	+	0.458273i	$0.151532\pi$
$307$			5.37830e44i			0.916546i	−0.888812	+	0.458273i	$0.848468\pi$
$308$	−1.63335e45	+	2.80044e44i	−2.62522	+	0.450105i
$309$	−2.24340e44			−0.340137
$310$	1.47256e43	+	1.73026e44i	0.0210651	+	0.247515i
$311$		−	1.27143e45i		−	1.71635i	−0.513353	−	0.858177i	$-0.671597\pi$
$311$		−	1.27143e45i		−	1.71635i	0.513353	−	0.858177i	$-0.328403\pi$
$312$	6.46965e43	+	2.48489e44i	0.0824324	+	0.316610i
$313$	−1.55517e44			−0.187059			−0.0935296	−	0.995616i	$-0.529815\pi$
$313$	−1.55517e44			−0.187059			−0.0935296	+	0.995616i	$0.529815\pi$
$314$	−7.76315e44	+	6.60693e43i	−0.881666	+	0.0750353i
$315$			2.17889e44i			0.233693i
$316$	−2.56999e44	−	1.49894e45i	−0.260354	−	1.51850i
$317$	−1.28628e45			−1.23103			−0.615515	−	0.788125i	$-0.711052\pi$
$317$	−1.28628e45			−1.23103			−0.615515	+	0.788125i	$0.711052\pi$
$318$	8.14779e43	+	9.57367e44i	0.0736804	+	0.865745i
$319$			1.38168e45i			1.18080i
$320$	4.14479e44	−	2.31521e44i	0.334813	−	0.187021i
$321$	3.50377e44			0.267575
$322$	1.64239e45	−	1.39777e44i	1.18596	−	0.100933i
$323$			1.98947e44i			0.135860i
$324$	−6.28017e44	+	1.07676e44i	−0.405659	+	0.0695520i
$325$	5.97368e44			0.365041
$326$	−1.14305e44	−	1.34308e45i	−0.0660918	−	0.776579i
$327$		−	1.77639e45i		−	0.972030i
$328$	3.02783e45	−	7.88324e44i	1.56820	−	0.408297i
$329$	−2.58264e45			−1.26630
$330$	1.14316e45	−	9.72899e43i	0.530708	−	0.0451666i
$331$			9.60496e44i			0.422271i	0.977457	+	0.211136i	$0.0677162\pi$
$331$			9.60496e44i			0.422271i	−0.977457	+	0.211136i	$0.932284\pi$
$332$	7.14671e44	+	4.16829e45i	0.297592	+	1.73569i
$333$	3.31281e44			0.130677
$334$	1.95308e44	+	2.29487e45i	0.0729933	+	0.857673i
$335$			9.16814e44i			0.324694i
$336$	3.14806e45	−	1.11219e45i	1.05666	−	0.373312i
$337$	2.40643e45			0.765658			0.382829	−	0.923819i	$-0.374950\pi$
$337$	2.40643e45			0.765658			0.382829	+	0.923819i	$0.374950\pi$
$338$	−2.69813e45	+	2.29628e44i	−0.813884	+	0.0692667i
$339$		−	4.09072e45i		−	1.17005i
$340$	1.18566e45	−	2.03286e44i	0.321616	−	0.0551425i
$341$	−4.57394e45			−1.17682
$342$	2.30585e43	+	2.70938e44i	0.00562809	+	0.0661301i
$343$		−	9.44676e44i		−	0.218771i
$344$	−1.02623e45	−	3.94159e45i	−0.225524	−	0.866202i
$345$	−1.14116e45			−0.238014
$346$	−3.27421e45	+	2.78656e44i	−0.648242	+	0.0551694i
$347$			5.95983e45i			1.12022i	0.828418	+	0.560110i	$0.189241\pi$
$347$			5.95983e45i			1.12022i	−0.828418	+	0.560110i	$0.810759\pi$
$348$	−4.70413e44	−	2.74366e45i	−0.0839562	−	0.489670i
$349$	3.96150e45			0.671432			0.335716	−	0.941963i	$-0.391022\pi$
$349$	3.96150e45			0.671432			0.335716	+	0.941963i	$0.391022\pi$
$350$	−6.58674e44	−	7.73943e45i	−0.106034	−	1.24590i
$351$			3.02867e45i			0.463152i
$352$	5.15047e45	+	1.13951e46i	0.748305	+	1.65557i
$353$	−3.77639e45			−0.521353			−0.260677	−	0.965426i	$-0.583946\pi$
$353$	−3.77639e45			−0.521353			−0.260677	+	0.965426i	$0.583946\pi$
$354$	−7.38564e45	+	6.28565e44i	−0.969013	+	0.0824691i
$355$		−	4.15144e45i		−	0.517712i
$356$	−5.95302e45	+	1.02067e45i	−0.705728	+	0.121000i
$357$	8.45983e45			0.953528
$358$	−1.09514e44	−	1.28679e45i	−0.0117375	−	0.137915i
$359$		−	8.40831e45i		−	0.857054i	−0.903529	−	0.428527i	$-0.859033\pi$
$359$		−	8.40831e45i		−	0.857054i	0.903529	−	0.428527i	$-0.140967\pi$
$360$	1.59113e45	−	4.14267e44i	0.154263	−	0.0401638i
$361$	1.05661e46			0.974504
$362$	−1.86574e46	+	1.58786e45i	−1.63718	+	0.139334i
$363$			2.10644e46i			1.75886i
$364$	−1.33430e45	−	7.78226e45i	−0.106030	−	0.618416i
$365$	−9.28601e45			−0.702357
$366$	3.54706e44	+	4.16780e45i	0.0255393	+	0.300087i
$367$		−	8.59773e45i		−	0.589379i	−0.955593	−	0.294689i	$-0.904784\pi$
$367$		−	8.59773e45i		−	0.589379i	0.955593	−	0.294689i	$-0.0952162\pi$
$368$	−4.14336e45	−	1.17278e46i	−0.270453	−	0.765517i
$369$	1.08355e46			0.673559
$370$	2.02911e45	−	1.72690e44i	0.120136	−	0.0102243i
$371$		−	2.95457e46i		−	1.66634i
$372$	9.08265e45	−	1.55726e45i	0.488022	−	0.0836736i
$373$	2.05825e46			1.05375			0.526876	−	0.849942i	$-0.323363\pi$
$373$	2.05825e46			1.05375			0.526876	+	0.849942i	$0.323363\pi$
$374$	2.68693e45	+	3.15714e46i	0.131089	+	1.54030i
$375$			1.16823e46i			0.543206i
$376$	4.91032e45	+	1.88597e46i	0.217635	+	0.835901i
$377$	−6.58318e45			−0.278158
$378$	3.92391e46	−	3.33949e45i	1.58076	−	0.134533i
$379$			2.71367e46i			1.04244i	0.853422	+	0.521221i	$0.174523\pi$
$379$			2.71367e46i			1.04244i	−0.853422	+	0.521221i	$0.825477\pi$
$380$	2.82468e44	+	1.64748e45i	0.0103482	+	0.0603553i
$381$	1.13484e46			0.396537
$382$	−3.46183e45	−	4.06765e46i	−0.115389	−	1.35582i
$383$			2.21749e46i			0.705152i	0.935783	+	0.352576i	$0.114694\pi$
$383$			2.21749e46i			0.705152i	−0.935783	+	0.352576i	$0.885306\pi$
$384$	−1.41071e46	−	2.08741e46i	−0.428031	−	0.633353i
$385$	−3.52794e46			−1.02148
$386$	2.60704e46	−	2.21875e45i	0.720404	−	0.0613109i
$387$		−	1.41056e46i		−	0.372043i
$388$	1.23050e46	−	2.10974e45i	0.309820	−	0.0531199i
$389$	−6.09024e46			−1.46400			−0.732001	−	0.681303i	$-0.761414\pi$
$389$	−6.09024e46			−1.46400			−0.732001	+	0.681303i	$0.761414\pi$
$390$	4.63549e44	+	5.44671e45i	0.0106398	+	0.125018i
$391$		−	3.15163e46i		−	0.690801i
$392$	−5.31267e46	+	1.38321e46i	−1.11215	+	0.289559i
$393$	−2.20251e46			−0.440405
$394$	2.67008e46	−	2.27241e45i	0.510027	−	0.0434065i
$395$		−	3.23763e46i		−	0.590852i
$396$	7.31842e45	+	4.26844e46i	0.127616	+	0.744313i
$397$	−8.96756e46			−1.49433			−0.747163	−	0.664641i	$-0.768585\pi$
$397$	−8.96756e46			−1.49433			−0.747163	+	0.664641i	$0.768585\pi$
$398$	−1.79715e45	−	2.11166e46i	−0.0286213	−	0.336301i
$399$			1.17550e46i			0.178942i
$400$	−5.52648e46	+	1.95248e46i	−0.804209	+	0.284123i
$401$	3.36429e46			0.468052			0.234026	−	0.972230i	$-0.424810\pi$
$401$	3.36429e46			0.468052			0.234026	+	0.972230i	$0.424810\pi$
$402$	4.84774e46	−	4.12573e45i	0.644868	−	0.0548823i
$403$		−	2.17931e46i		−	0.277222i
$404$	3.51660e46	−	6.02937e45i	0.427817	−	0.0733512i
$405$	−1.35649e46			−0.157843
$406$	7.25879e45	+	8.52909e46i	0.0807971	+	0.949367i
$407$			5.36393e46i			0.571195i
$408$	−1.60845e46	−	6.17779e46i	−0.163879	−	0.629434i
$409$	6.55074e46			0.638661			0.319331	−	0.947643i	$-0.396542\pi$
$409$	6.55074e46			0.638661			0.319331	+	0.947643i	$0.396542\pi$
$410$	6.63680e46	−	5.64833e45i	0.619226	−	0.0527000i
$411$		−	1.86433e46i		−	0.166483i
$412$	−8.79683e45	−	5.13071e46i	−0.0751928	−	0.438559i
$413$	2.27931e47			1.86510
$414$	−3.65282e45	−	4.29207e46i	−0.0286169	−	0.336249i
$415$			9.00329e46i			0.675360i
$416$	−5.42931e46	+	2.45400e46i	−0.390000	+	0.176277i
$417$	1.54580e47			1.06342
$418$	−4.38688e46	+	3.73351e45i	−0.289057	+	0.0246005i
$419$		−	3.50715e46i		−	0.221361i	−0.993856	−	0.110681i	$-0.964697\pi$
$419$		−	3.50715e46i		−	0.221361i	0.993856	−	0.110681i	$-0.0353031\pi$
$420$	7.00558e46	−	1.20114e46i	0.423601	−	0.0726283i
$421$	4.57681e46			0.265146			0.132573	−	0.991173i	$-0.457676\pi$
$421$	4.57681e46			0.265146			0.132573	+	0.991173i	$0.457676\pi$
$422$	−1.13567e45	−	1.33442e46i	−0.00630418	−	0.0740742i
$423$			6.74925e46i			0.359028i
$424$	−2.15757e47	+	5.61745e46i	−1.09997	+	0.286387i
$425$	−1.48514e47			−0.725717
$426$	−2.19511e47	+	1.86818e46i	−1.02822	+	0.0875076i
$427$		−	1.28624e47i		−	0.577591i
$428$	1.37390e46	+	8.01321e46i	0.0591517	+	0.345000i
$429$	−1.43984e47			−0.594404
$430$	−7.35292e45	−	8.63970e46i	−0.0291090	−	0.342032i
$431$			1.74245e47i			0.661561i	0.943708	+	0.330780i	$0.107312\pi$
$431$			1.74245e47i			0.661561i	−0.943708	+	0.330780i	$0.892688\pi$
$432$	−9.89910e46	−	2.80194e47i	−0.360486	−	1.02035i
$433$	2.39178e47			0.835486			0.417743	−	0.908565i	$-0.362821\pi$
$433$	2.39178e47			0.835486			0.417743	+	0.908565i	$0.362821\pi$
$434$	−2.82348e47	+	2.40296e46i	−0.946172	+	0.0805252i
$435$		−	5.92617e46i		−	0.190532i
$436$	4.06265e47	−	6.96560e46i	1.25329	−	0.214883i
$437$	4.37922e46			0.129638
$438$	4.17878e46	+	4.91007e47i	0.118718	+	1.39493i
$439$		−	4.04214e47i		−	1.10217i	−0.834448	−	0.551087i	$-0.814213\pi$
$439$		−	4.04214e47i		−	1.10217i	0.834448	−	0.551087i	$-0.185787\pi$
$440$	6.70760e46	+	2.57628e47i	0.175557	+	0.674287i
$441$	−1.90122e47			−0.477680
$442$	−1.50426e47	+	1.28022e46i	−0.362845	+	0.0308804i
$443$		−	6.19474e46i		−	0.143468i	−0.997424	−	0.0717341i	$-0.977147\pi$
$443$		−	6.19474e46i		−	0.143468i	0.997424	−	0.0717341i	$-0.0228533\pi$
$444$	−1.82623e46	−	1.06514e47i	−0.0406126	−	0.236871i
$445$	−1.28582e47			−0.274600
$446$	−6.98867e46	−	8.21169e47i	−0.143340	−	1.68424i
$447$		−	3.29873e47i		−	0.649848i
$448$	3.77802e47	+	6.76357e47i	0.714925	+	1.27989i
$449$	−5.94487e47			−1.08071			−0.540354	−	0.841438i	$-0.681710\pi$
$449$	−5.94487e47			−1.08071			−0.540354	+	0.841438i	$0.681710\pi$
$450$	−2.02255e47	+	1.72132e46i	−0.353244	+	0.0300633i
$451$			1.75443e48i			2.94415i
$452$	9.35557e47	−	1.60405e47i	1.50862	−	0.258659i
$453$	−6.53263e47			−1.01233
$454$	−5.65019e46	−	6.63899e47i	−0.0841508	−	0.988773i
$455$		−	1.68093e47i		−	0.240627i
$456$	8.58410e46	−	2.23496e46i	0.118121	−	0.0307540i
$457$	2.64756e47			0.350231			0.175116	−	0.984548i	$-0.443970\pi$
$457$	2.64756e47			0.350231			0.175116	+	0.984548i	$0.443970\pi$
$458$	8.06303e47	−	6.86214e46i	1.02546	−	0.0872733i
$459$		−	7.52970e47i		−	0.920766i
$460$	−4.47472e46	−	2.60986e47i	−0.0526169	−	0.306886i
$461$	6.93782e47			0.784524			0.392262	−	0.919854i	$-0.371693\pi$
$461$	6.93782e47			0.784524			0.392262	+	0.919854i	$0.371693\pi$
$462$	1.58760e47	+	1.86543e48i	0.172658	+	2.02873i
$463$		−	1.29767e48i		−	1.35740i	−0.734417	−	0.678698i	$-0.762544\pi$
$463$		−	1.29767e48i		−	1.35740i	0.734417	−	0.678698i	$-0.237456\pi$
$464$	6.09036e47	−	2.15169e47i	0.612800	−	0.216499i
$465$	1.96181e47			0.189891
$466$	1.90991e47	−	1.62545e46i	0.177855	−	0.0151366i
$467$			6.13925e47i			0.550062i	0.961435	+	0.275031i	$0.0886881\pi$
$467$			6.13925e47i			0.550062i	−0.961435	+	0.275031i	$0.911312\pi$
$468$	−2.03375e47	+	3.48695e46i	−0.175336	+	0.0300622i
$469$	−1.49608e48			−1.24121
$470$	3.51824e46	+	4.13393e47i	0.0280908	+	0.330067i
$471$			8.80203e47i			0.676404i
$472$	−4.33360e47	−	1.66447e48i	−0.320548	−	1.23117i
$473$	2.28390e48			1.62621
$474$	−1.71193e48	+	1.45696e47i	−1.17348	+	0.0998703i
$475$		−	2.06362e47i		−	0.136190i
$476$	3.31727e47	+	1.93478e48i	0.210793	+	1.22944i
$477$	−7.72120e47			−0.472448
$478$	−7.46229e46	−	8.76820e47i	−0.0439713	−	0.516664i
$479$			2.23667e47i			0.126929i	0.997984	+	0.0634646i	$0.0202150\pi$
$479$			2.23667e47i			0.126929i	−0.997984	+	0.0634646i	$0.979785\pi$
$480$	−2.20909e47	−	4.88746e47i	−0.120745	−	0.267141i
$481$	−2.55571e47			−0.134555
$482$	5.53290e47	−	4.70884e46i	0.280612	−	0.0238818i
$483$		−	1.86218e48i		−	0.909855i
$484$	−4.81748e48	+	8.25979e47i	−2.26780	+	0.388824i
$485$	2.65781e47			0.120551
$486$	−1.48919e47	−	1.74979e48i	−0.0650872	−	0.764776i
$487$			2.09873e48i			0.883967i	0.897023	+	0.441984i	$0.145725\pi$
$487$			2.09873e48i			0.883967i	−0.897023	+	0.441984i	$0.854275\pi$
$488$	−9.39278e47	+	2.44550e47i	−0.381274	+	0.0992684i
$489$	−1.52282e48			−0.595783
$490$	−1.16450e48	+	9.91064e46i	−0.439148	+	0.0373742i
$491$		−	9.13688e47i		−	0.332148i	−0.986113	−	0.166074i	$-0.946891\pi$
$491$		−	9.13688e47i		−	0.332148i	0.986113	−	0.166074i	$-0.0531090\pi$
$492$	−5.97322e47	−	3.48385e48i	−0.209332	−	1.22092i
$493$	1.63667e48			0.552990
$494$	−1.77888e46	−	2.09018e47i	−0.00579510	−	0.0680925i
$495$			9.21961e47i			0.289614i
$496$	7.12299e47	+	2.01616e48i	0.215770	+	0.610738i
$497$	6.77442e48			1.97905
$498$	4.76058e48	−	4.05155e47i	1.34132	−	0.114155i
$499$			3.32131e47i			0.0902609i	0.998981	+	0.0451304i	$0.0143703\pi$
$499$			3.32131e47i			0.0902609i	−0.998981	+	0.0451304i	$0.985630\pi$
$500$	−2.67176e48	+	4.58086e47i	−0.700387	+	0.120084i
$501$	2.60197e48			0.657997
$502$	2.43774e47	+	2.86435e48i	0.0594731	+	0.698810i
$503$			3.11350e48i			0.732868i	0.930444	+	0.366434i	$0.119421\pi$
$503$			3.11350e48i			0.732868i	−0.930444	+	0.366434i	$0.880579\pi$
$504$	6.76011e47	+	2.59645e48i	0.153534	+	0.589699i
$505$	7.59568e47			0.166465
$506$	6.94950e48	−	5.91446e47i	1.46975	−	0.125085i
$507$			3.05920e48i			0.624403i
$508$	4.44993e47	+	2.59540e48i	0.0876609	+	0.511278i
$509$	−6.15463e48			−1.17026			−0.585129	−	0.810940i	$-0.698956\pi$
$509$	−6.15463e48			−1.17026			−0.585129	+	0.810940i	$0.698956\pi$
$510$	−1.15245e47	−	1.35413e48i	−0.0211524	−	0.248541i
$511$		−	1.51531e49i		−	2.68489i
$512$	4.22079e48	−	4.04484e48i	0.721995	−	0.691898i
$513$	1.04626e48			0.172793
$514$	−1.31885e48	+	1.12242e47i	−0.210309	+	0.0178986i
$515$		−	1.10821e48i		−	0.170644i
$516$	−4.53523e48	+	7.77586e47i	−0.674381	+	0.115626i
$517$	−1.09280e49			−1.56932
$518$	2.81799e47	+	3.31115e48i	0.0390845	+	0.459243i
$519$			3.71237e48i			0.497324i
$520$	−1.22750e48	+	3.19591e47i	−0.158840	+	0.0413557i
$521$	−5.37366e48			−0.671725			−0.335862	−	0.941911i	$-0.609028\pi$
$521$	−5.37366e48			−0.671725			−0.335862	+	0.941911i	$0.609028\pi$
$522$	2.22892e48	−	1.89695e47i	0.269169	−	0.0229079i
$523$			1.04564e49i			1.21998i	0.792411	+	0.609988i	$0.208826\pi$
$523$			1.04564e49i			1.21998i	−0.792411	+	0.609988i	$0.791174\pi$
$524$	−8.63649e47	−	5.03719e48i	−0.0973585	−	0.567839i
$525$	−8.77513e48			−0.955842
$526$	−4.93547e47	−	5.79919e48i	−0.0519500	−	0.610413i
$527$			5.41807e48i			0.551129i
$528$	1.33205e49	−	4.70606e48i	1.30951	−	0.462643i
$529$	3.58716e48			0.340839
$530$	−4.72925e48	+	4.02489e47i	−0.434337	+	0.0369648i
$531$		−	5.95655e48i		−	0.528802i
$532$	−2.68840e48	+	4.60938e47i	−0.230720	+	0.0395579i
$533$	−8.35921e48			−0.693546
$534$	5.78630e47	+	6.79891e48i	0.0464150	+	0.545377i
$535$			1.73081e48i			0.134240i
$536$	2.84446e48	+	1.09251e49i	0.213321	+	0.819332i
$537$	−1.45899e48			−0.105807
$538$	−6.29640e48	+	5.35863e47i	−0.441582	+	0.0375814i
$539$		−	3.07836e49i		−	2.08796i
$540$	−1.06908e48	−	6.23535e48i	−0.0701329	−	0.409047i
$541$	1.77918e49			1.12894			0.564468	−	0.825455i	$-0.309081\pi$
$541$	1.77918e49			1.12894			0.564468	+	0.825455i	$0.309081\pi$
$542$	1.07384e48	+	1.26176e49i	0.0659100	+	0.774444i
$543$			2.11541e49i			1.25602i
$544$	1.34980e49	−	6.10099e48i	0.775337	−	0.350445i
$545$	8.77513e48			0.487659
$546$	−8.88808e48	+	7.56431e47i	−0.477904	+	0.0406726i
$547$			3.11538e48i			0.162084i	0.996711	+	0.0810419i	$0.0258248\pi$
$547$			3.11538e48i			0.162084i	−0.996711	+	0.0810419i	$0.974175\pi$
$548$	4.26377e48	−	7.31042e47i	0.214656	−	0.0368038i
$549$	−3.36135e48			−0.163761
$550$	−2.78707e48	−	3.27481e49i	−0.131407	−	1.54404i
$551$			2.27417e48i			0.103776i
$552$	−1.35985e49	+	3.54051e48i	−0.600605	+	0.156373i
$553$	5.28324e49			2.25865
$554$	−2.63500e49	+	2.24255e48i	−1.09045	+	0.0928041i
$555$		−	2.30065e48i		−	0.0921671i
$556$	6.06141e48	+	3.53529e49i	0.235086	+	1.37113i
$557$	−2.68438e49			−1.00798			−0.503988	−	0.863711i	$-0.668134\pi$
$557$	−2.68438e49			−1.00798			−0.503988	+	0.863711i	$0.668134\pi$
$558$	6.27968e47	+	7.37864e48i	0.0228309	+	0.268263i
$559$			1.08819e49i			0.383083i
$560$	5.49406e48	+	1.55509e49i	0.187288	+	0.530118i
$561$	3.57964e49			1.18170
$562$	−2.84319e49	+	2.41973e48i	−0.908975	+	0.0773595i
$563$		−	5.69125e48i		−	0.176221i	−0.996111	−	0.0881103i	$-0.971917\pi$
$563$		−	5.69125e48i		−	0.176221i	0.996111	−	0.0881103i	$-0.0280828\pi$
$564$	2.17002e49	−	3.72060e48i	0.650790	−	0.111581i
$565$	2.02076e49			0.587005
$566$	−4.64908e48	−	5.46267e49i	−0.130819	−	1.53713i
$567$		−	2.21355e49i		−	0.603384i
$568$	−1.28801e49	−	4.94702e49i	−0.340132	−	1.30639i
$569$	−1.13238e49			−0.289714			−0.144857	−	0.989453i	$-0.546272\pi$
$569$	−1.13238e49			−0.289714			−0.144857	+	0.989453i	$0.546272\pi$
$570$	1.88158e48	−	1.60134e47i	0.0466418	−	0.00396951i
$571$			4.77390e49i			1.14663i	0.819335	+	0.573315i	$0.194343\pi$
$571$			4.77390e49i			1.14663i	−0.819335	+	0.573315i	$0.805657\pi$
$572$	−5.64589e48	−	3.29294e49i	−0.131403	−	0.766399i
$573$	−4.61199e49			−1.04017
$574$	9.21709e48	+	1.08301e50i	0.201456	+	2.36711i
$575$			3.26909e49i			0.692478i
$576$	1.76753e49	−	9.87315e48i	0.362879	−	0.202699i
$577$	4.06405e49			0.808714			0.404357	−	0.914601i	$-0.367495\pi$
$577$	4.06405e49			0.808714			0.404357	+	0.914601i	$0.367495\pi$
$578$	−1.42596e49	+	1.21358e48i	−0.275046	+	0.0234081i
$579$		−	2.95592e49i		−	0.552686i
$580$	1.35533e49	−	2.32377e48i	0.245664	−	0.0421201i
$581$	−1.46918e50			−2.58169
$582$	−1.19603e48	−	1.40534e49i	−0.0203765	−	0.239424i
$583$		−	1.25018e50i		−	2.06508i
$584$	−1.10656e50	+	2.88103e49i	−1.77232	+	0.461442i
$585$	−4.39279e48			−0.0682236
$586$	3.37575e49	−	2.87297e48i	0.508409	−	0.0432688i
$587$			5.94523e49i			0.868326i	0.900834	+	0.434163i	$0.142956\pi$
$587$			5.94523e49i			0.868326i	−0.900834	+	0.434163i	$0.857044\pi$
$588$	1.04807e49	+	6.11282e49i	0.148456	+	0.865864i
$589$	−7.52846e48			−0.103426
$590$	−3.10502e48	−	3.64840e49i	−0.0413741	−	0.486146i
$591$		−	3.02740e49i		−	0.391287i
$592$	2.36439e49	−	8.35325e48i	0.296434	−	0.104728i
$593$	−1.47365e49			−0.179230			−0.0896148	−	0.995976i	$-0.528564\pi$
$593$	−1.47365e49			−0.179230			−0.0896148	+	0.995976i	$0.528564\pi$
$594$	1.66034e50	−	1.41305e49i	1.95903	−	0.166725i
$595$			4.17903e49i			0.478377i
$596$	7.54428e49	−	1.29350e49i	0.837886	−	0.143659i
$597$	−2.39424e49			−0.258006
$598$	2.81801e48	+	3.31117e49i	0.0294660	+	0.346226i
$599$		−	2.00221e49i		−	0.203154i	−0.994828	−	0.101577i	$-0.967611\pi$
$599$		−	2.00221e49i		−	0.203154i	0.994828	−	0.101577i	$-0.0323889\pi$
$600$	1.66840e49	+	6.40804e49i	0.164277	+	0.630961i
$601$	1.56279e50			1.49334			0.746670	−	0.665195i	$-0.231651\pi$
$601$	1.56279e50			1.49334			0.746670	+	0.665195i	$0.231651\pi$
$602$	1.40985e50	−	1.19987e49i	1.30748	−	0.111275i
$603$			3.90972e49i			0.351912i
$604$	−2.56158e49	−	1.49403e50i	−0.223791	−	1.30525i
$605$	−1.04055e50			−0.882404
$606$	−3.41812e48	−	4.01629e49i	−0.0281371	−	0.330611i
$607$			1.63488e50i			1.30644i	0.757168	+	0.653220i	$0.226582\pi$
$607$			1.63488e50i			1.30644i	−0.757168	+	0.653220i	$0.773418\pi$
$608$	8.47740e48	+	1.87557e49i	0.0657655	+	0.145502i
$609$	9.67047e49			0.728344
$610$	−2.05883e49	+	1.75220e48i	−0.150551	+	0.0128129i
$611$		−	5.20679e49i		−	0.369682i
$612$	5.05619e49	−	8.66905e48i	0.348576	−	0.0597649i
$613$	−9.89772e49			−0.662593			−0.331296	−	0.943527i	$-0.607486\pi$
$613$	−9.89772e49			−0.662593			−0.331296	+	0.943527i	$0.607486\pi$
$614$	1.19558e49	+	1.40481e50i	0.0777228	+	0.913244i
$615$		−	7.52495e49i		−	0.475063i
$616$	−4.20404e50	+	1.09456e50i	−2.57759	+	0.671101i
$617$	1.30487e50			0.777022			0.388511	−	0.921444i	$-0.372990\pi$
$617$	1.30487e50			0.777022			0.388511	+	0.921444i	$0.372990\pi$
$618$	−5.85976e49	+	4.98702e48i	−0.338912	+	0.0288436i
$619$		−	2.95569e49i		−	0.166046i	−0.996548	−	0.0830228i	$-0.973543\pi$
$619$		−	2.95569e49i		−	0.166046i	0.996548	−	0.0830228i	$-0.0264574\pi$
$620$	7.69265e48	+	4.48670e49i	0.0419784	+	0.244837i
$621$	−1.65744e50			−0.878594
$622$	−2.82637e49	−	3.32098e50i	−0.145546	−	1.71017i
$623$		−	2.09824e50i		−	1.04971i
$624$	2.24225e49	+	6.34670e49i	0.108984	+	0.308479i
$625$	1.22905e50			0.580401
$626$	−4.06209e49	+	3.45710e48i	−0.186385	+	0.0158626i
$627$			4.97395e49i			0.221761i
$628$	−2.01304e50	+	3.45145e49i	−0.872127	+	0.149530i
$629$	6.35386e49			0.267501
$630$	4.84361e48	+	5.69125e49i	0.0198171	+	0.232851i
$631$			1.95097e50i			0.775751i	0.921712	+	0.387876i	$0.126791\pi$
$631$			1.95097e50i			0.775751i	−0.921712	+	0.387876i	$0.873209\pi$
$632$	−1.00449e50	−	3.85809e50i	−0.388185	−	1.49095i
$633$	−1.51299e49			−0.0568289
$634$	−3.35976e50	+	2.85937e49i	−1.22660	+	0.104391i
$635$			5.60593e49i			0.198939i
$636$	4.25640e49	+	2.48253e50i	0.146830	+	0.856379i
$637$	1.46672e50			0.491855
$638$	3.07144e49	+	3.60895e50i	0.100131	+	1.17654i
$639$		−	1.77037e50i		−	0.561109i
$640$	1.03115e50	−	6.96871e49i	0.317748	−	0.214740i
$641$	2.40479e50			0.720498			0.360249	−	0.932856i	$-0.382692\pi$
$641$	2.40479e50			0.720498			0.360249	+	0.932856i	$0.382692\pi$
$642$	9.15185e49	−	7.78880e48i	0.266611	−	0.0226903i
$643$		−	3.65575e50i		−	1.03557i	−0.855511	−	0.517785i	$-0.826757\pi$
$643$		−	3.65575e50i		−	1.03557i	0.855511	−	0.517785i	$-0.173243\pi$
$644$	4.25884e50	−	7.30197e49i	1.17313	−	0.201138i
$645$	−9.79588e49			−0.262403
$646$	4.42254e48	+	5.19649e49i	0.0115209	+	0.135371i
$647$			7.82816e50i			1.98327i	0.129059	+	0.991637i	$0.458804\pi$
$647$			7.82816e50i			1.98327i	−0.129059	+	0.991637i	$0.541196\pi$
$648$	−1.61644e50	+	4.20857e49i	−0.398300	+	0.103701i
$649$	9.64454e50			2.31141
$650$	1.56032e50	−	1.32793e49i	0.363726	−	0.0309553i
$651$			3.20133e50i			0.725893i
$652$	−5.97127e49	−	3.48272e50i	−0.131707	−	0.768177i
$653$	−7.97111e50			−1.71034			−0.855169	−	0.518350i	$-0.826547\pi$
$653$	−7.97111e50			−1.71034			−0.855169	+	0.518350i	$0.826547\pi$
$654$	−3.94888e49	−	4.63993e50i	−0.0824278	−	0.968528i
$655$		−	1.08801e50i		−	0.220947i
$656$	7.73343e50	−	2.73218e50i	1.52793	−	0.539809i
$657$	−3.95999e50			−0.761232
$658$	−6.74586e50	+	5.74115e49i	−1.26174	+	0.107382i
$659$		−	7.45713e50i		−	1.35717i	−0.734522	−	0.678585i	$-0.762593\pi$
$659$		−	7.45713e50i		−	1.35717i	0.734522	−	0.678585i	$-0.237407\pi$
$660$	2.96430e50	−	5.08242e49i	0.524966	−	0.0900077i
$661$	−3.41956e50			−0.589310			−0.294655	−	0.955604i	$-0.595205\pi$
$661$	−3.41956e50			−0.589310			−0.294655	+	0.955604i	$0.595205\pi$
$662$	2.13516e49	+	2.50881e50i	0.0358085	+	0.420750i
$663$			1.70556e50i			0.278371i
$664$	2.79332e50	+	1.07287e51i	0.443706	+	1.70420i
$665$	−5.80681e49			−0.0897735
$666$	8.65305e49	−	7.36429e48i	0.130207	−	0.0110814i
$667$		−	3.60264e50i		−	0.527662i
$668$	1.02029e50	+	5.95078e50i	0.145461	+	0.848394i
$669$	−9.31060e50			−1.29213
$670$	2.03805e49	+	2.39472e50i	0.0275340	+	0.323525i
$671$		−	5.44252e50i		−	0.715805i
$672$	7.97548e50	−	3.60484e50i	1.02120	−	0.461572i
$673$	8.55644e50			1.06665			0.533325	−	0.845911i	$-0.320942\pi$
$673$	8.55644e50			1.06665			0.533325	+	0.845911i	$0.320942\pi$
$674$	6.28559e50	−	5.34943e49i	0.762900	−	0.0649276i
$675$			7.81034e50i			0.923001i
$676$	−6.99647e50	+	1.19958e50i	−0.805079	+	0.138034i
$677$	−8.83947e50			−0.990444			−0.495222	−	0.868766i	$-0.664913\pi$
$677$	−8.83947e50			−0.990444			−0.495222	+	0.868766i	$0.664913\pi$
$678$	−9.09356e49	−	1.06849e51i	−0.0992201	−	1.16584i
$679$			4.33708e50i			0.460831i
$680$	3.05174e50	−	7.94550e49i	0.315782	−	0.0822169i
$681$	−7.52743e50			−0.758575
$682$	−1.19471e51	+	1.01677e50i	−1.17258	+	0.0997943i
$683$		−	1.05574e50i		−	0.100922i	−0.998726	−	0.0504608i	$-0.983931\pi$
$683$		−	1.05574e50i		−	0.100922i	0.998726	−	0.0504608i	$-0.0160690\pi$
$684$	1.20457e49	+	7.02563e49i	0.0112156	+	0.0654147i
$685$	9.20953e49			0.0835232
$686$	−2.09999e49	−	2.46749e50i	−0.0185517	−	0.217983i
$687$		−	9.14204e50i		−	0.786723i
$688$	−3.55672e50	−	1.00673e51i	−0.298165	−	0.843957i
$689$	5.95661e50			0.486467
$690$	−2.98071e50	+	2.53677e49i	−0.237157	+	0.0201836i
$691$			4.73080e50i			0.366716i	0.983046	+	0.183358i	$0.0586967\pi$
$691$			4.73080e50i			0.366716i	−0.983046	+	0.183358i	$0.941303\pi$
$692$	−8.49029e50	+	1.45570e50i	−0.641228	+	0.109941i
$693$	−1.50448e51			−1.10710
$694$	1.32485e50	+	1.55671e51i	0.0949943	+	1.11618i
$695$			7.63605e50i			0.533510i
$696$	−1.83862e50	−	7.06186e50i	−0.125178	−	0.480787i
$697$	2.07822e51			1.37880
$698$	1.03474e51	−	8.80631e49i	0.669013	−	0.0569372i
$699$		−	2.16550e50i		−	0.136448i
$700$	−3.44091e50	−	2.00689e51i	−0.211304	−	1.23242i
$701$	1.72691e51			1.03358			0.516791	−	0.856112i	$-0.327127\pi$
$701$	1.72691e51			1.03358			0.516791	+	0.856112i	$0.327127\pi$
$702$	6.73265e49	+	7.91087e50i	0.0392752	+	0.461484i
$703$			8.82876e49i			0.0502000i
$704$	1.59861e51	+	2.86189e51i	0.886002	+	1.58615i
$705$	4.68714e50			0.253224
$706$	−9.86392e50	+	8.39482e49i	−0.519475	+	0.0442106i
$707$			1.23948e51i			0.636343i
$708$	−1.91516e51	+	3.28362e50i	−0.958529	+	0.164344i
$709$	3.74194e51			1.82585			0.912924	−	0.408130i	$-0.133819\pi$
$709$	3.74194e51			1.82585			0.912924	+	0.408130i	$0.133819\pi$
$710$	−9.22854e49	−	1.08435e51i	−0.0439018	−	0.515847i
$711$		−	1.38067e51i		−	0.640381i
$712$	−1.53224e51	+	3.98933e50i	−0.692925	+	0.180410i
$713$	1.19262e51			0.525886
$714$	2.20970e51	−	1.88060e50i	0.950094	−	0.0808589i
$715$		−	7.11258e50i		−	0.298208i
$716$	−5.72099e49	−	3.33674e50i	−0.0233904	−	0.136423i
$717$	−9.94158e50			−0.396379
$718$	−1.86914e50	−	2.19625e51i	−0.0726780	−	0.853967i
$719$		−	3.21231e50i		−	0.121814i	−0.998143	−	0.0609070i	$-0.980601\pi$
$719$		−	3.21231e50i		−	0.121814i	0.998143	−	0.0609070i	$-0.0193993\pi$
$720$	4.06394e50	−	1.43577e50i	0.150301	−	0.0531006i
$721$	1.80840e51			0.652319
$722$	2.75985e51	−	2.34881e50i	0.970994	−	0.0826377i
$723$		−	6.27332e50i		−	0.215282i
$724$	−4.83800e51	+	8.29496e50i	−1.61946	+	0.277664i
$725$	−1.69767e51			−0.554332
$726$	4.68257e50	+	5.50202e51i	0.149151	+	1.75252i
$727$			2.83677e51i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$727$			2.83677e51i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$728$	−5.21517e50	−	2.00306e51i	−0.158090	−	0.607198i
$729$	−3.37566e51			−0.998306
$730$	−2.42550e51	+	2.06426e50i	−0.699827	+	0.0595596i
$731$		−	2.70540e51i		−	0.761585i
$732$	1.85298e50	+	1.08074e51i	0.0508946	+	0.296841i
$733$	−4.57843e51			−1.22700			−0.613500	−	0.789695i	$-0.710239\pi$
$733$	−4.57843e51			−1.22700			−0.613500	+	0.789695i	$0.710239\pi$
$734$	−1.91125e50	−	2.24572e51i	−0.0499792	−	0.587256i
$735$			1.32034e51i			0.336909i
$736$	−1.34295e51	−	2.97119e51i	−0.334395	−	0.739825i
$737$	−6.33042e51			−1.53822
$738$	2.83024e51	−	2.40871e50i	0.671133	−	0.0571176i
$739$			1.18843e51i			0.275026i	0.990500	+	0.137513i	$0.0439108\pi$
$739$			1.18843e51i			0.275026i	−0.990500	+	0.137513i	$0.956089\pi$
$740$	5.26163e50	−	9.02130e49i	0.118836	−	0.0203750i
$741$	−2.36990e50			−0.0522398
$742$	−6.56792e50	−	7.71732e51i	−0.141305	−	1.66034i
$743$			1.36253e51i			0.286119i	0.989714	+	0.143059i	$0.0456940\pi$
$743$			1.36253e51i			0.286119i	−0.989714	+	0.143059i	$0.954306\pi$
$744$	2.33777e51	−	6.08661e50i	0.479169	−	0.124756i
$745$	1.62953e51			0.326023
$746$	5.37613e51	−	4.57543e50i	1.04996	−	0.0893578i
$747$			3.83942e51i			0.731973i
$748$	1.40365e51	+	8.18672e51i	0.261234	+	1.52364i
$749$	−2.82439e51			−0.513158
$750$	2.59694e50	+	3.05141e51i	0.0460637	+	0.541250i
$751$		−	9.12443e51i		−	1.58011i	−0.613037	−	0.790054i	$-0.710052\pi$
$751$		−	9.12443e51i		−	1.58011i	0.613037	−	0.790054i	$-0.289948\pi$
$752$	1.70182e51	+	4.81701e51i	0.287735	+	0.814434i
$753$	3.24766e51			0.536119
$754$	−1.71952e51	+	1.46342e50i	−0.277156	+	0.0235877i
$755$		−	3.22703e51i		−	0.507876i
$756$	1.01750e52	−	1.74455e51i	1.56366	−	0.268096i
$757$	1.02914e52			1.54436			0.772181	−	0.635403i	$-0.219166\pi$
$757$	1.02914e52			1.54436			0.772181	+	0.635403i	$0.219166\pi$
$758$	6.03242e50	+	7.08810e51i	0.0883987	+	1.03869i
$759$		−	7.87949e51i		−	1.12758i
$760$	1.10404e50	+	4.24042e50i	0.0154290	+	0.0592604i
$761$	−6.32974e51			−0.863898			−0.431949	−	0.901898i	$-0.642174\pi$
$761$	−6.32974e51			−0.863898			−0.431949	+	0.901898i	$0.642174\pi$
$762$	2.96419e51	−	2.52271e50i	0.395109	−	0.0336262i
$763$			1.43195e52i			1.86417i
$764$	−1.80846e51	−	1.05477e52i	−0.229947	−	1.34115i
$765$	1.09211e51			0.135632
$766$	4.92941e50	+	5.79207e51i	0.0597967	+	0.702612i
$767$			4.59525e51i			0.544494i
$768$	−4.14880e51	−	5.13871e51i	−0.480198	−	0.594774i
$769$	−2.74311e51			−0.310148			−0.155074	−	0.987903i	$-0.549562\pi$
$769$	−2.74311e51			−0.310148			−0.155074	+	0.987903i	$0.549562\pi$
$770$	−9.21498e51	+	7.84253e50i	−1.01780	+	0.0866210i
$771$			1.49534e51i			0.161347i
$772$	6.76026e51	−	1.15908e51i	0.712610	−	0.122180i
$773$	−8.35558e51			−0.860490			−0.430245	−	0.902712i	$-0.641573\pi$
$773$	−8.35558e51			−0.860490			−0.430245	+	0.902712i	$0.641573\pi$
$774$	−3.13563e50	−	3.68437e51i	−0.0315491	−	0.370703i
$775$		−	5.62000e51i		−	0.552466i
$776$	3.16715e51	−	8.24599e50i	0.304199	−	0.0792012i
$777$	3.75425e51			0.352326
$778$	−1.59077e52	+	1.35385e51i	−1.45873	+	0.124147i
$779$			2.88771e51i			0.258749i
$780$	2.42158e50	+	1.41237e51i	0.0212029	+	0.123665i
$781$	2.86649e52			2.45263
$782$	−7.00598e50	−	8.23204e51i	−0.0585798	−	0.688313i
$783$		−	8.60724e51i		−	0.703319i
$784$	−1.35692e52	+	4.79392e51i	−1.08359	+	0.382826i
$785$	−4.34808e51			−0.339346
$786$	−5.75295e51	+	4.89612e50i	−0.438818	+	0.0373462i
$787$		−	1.35932e52i		−	1.01339i	−0.862125	−	0.506696i	$-0.830867\pi$
$787$		−	1.35932e52i		−	1.01339i	0.862125	−	0.506696i	$-0.169133\pi$
$788$	6.92374e51	−	1.18711e51i	0.504509	−	0.0865003i
$789$	−6.57525e51			−0.468302
$790$	−7.19716e50	−	8.45667e51i	−0.0501041	−	0.588724i
$791$			3.29752e52i			2.24394i
$792$	2.86043e51	+	1.09865e52i	0.190274	+	0.730810i
$793$	2.59315e51			0.168621
$794$	−2.34233e52	+	1.99347e51i	−1.48894	+	0.126718i
$795$			5.36213e51i			0.333219i
$796$	−9.38831e50	−	5.47569e51i	−0.0570364	−	0.332662i
$797$	8.02228e51			0.476484			0.238242	−	0.971206i	$-0.423429\pi$
$797$	8.02228e51			0.476484			0.238242	+	0.971206i	$0.423429\pi$
$798$	2.61311e50	+	3.07041e51i	0.0151742	+	0.178297i
$799$			1.29448e52i			0.734944i
$800$	−1.40011e52	+	6.32839e51i	−0.777219	+	0.351296i
$801$	−5.48335e51			−0.297619
$802$	8.78751e51	−	7.47872e50i	0.466366	−	0.0396907i
$803$		−	6.41181e52i		−	3.32737i
$804$	1.25706e52	−	2.15528e51i	0.637891	−	0.109369i
$805$	9.19888e51			0.456467
$806$	−4.84454e50	−	5.69234e51i	−0.0235083	−	0.276223i
$807$			7.13900e51i			0.338777i
$808$	9.05132e51	−	2.35660e51i	0.420056	−	0.109366i
$809$	−2.33922e52			−1.06169			−0.530844	−	0.847469i	$-0.678125\pi$
$809$	−2.33922e52			−1.06169			−0.530844	+	0.847469i	$0.678125\pi$
$810$	−3.54314e51	+	3.01543e50i	−0.157274	+	0.0133850i
$811$			2.42897e52i			1.05450i	0.849710	+	0.527250i	$0.176777\pi$
$811$			2.42897e52i			1.05450i	−0.849710	+	0.527250i	$0.823223\pi$
$812$	3.79199e51	+	2.21166e52i	0.161012	+	0.939096i
$813$	1.43061e52			0.594145
$814$	1.19239e51	+	1.40106e52i	0.0484371	+	0.569137i
$815$		−	7.52249e51i		−	0.298899i
$816$	−5.57457e51	−	1.57788e52i	−0.216665	−	0.613270i
$817$	3.75918e51			0.142921
$818$	1.71105e52	−	1.45621e51i	0.636361	−	0.0541583i
$819$		−	7.16827e51i		−	0.260798i
$820$	1.72097e52	−	2.95069e51i	0.612526	−	0.105020i
$821$	1.13894e52			0.396575			0.198288	−	0.980144i	$-0.436462\pi$
$821$	1.13894e52			0.396575			0.198288	+	0.980144i	$0.436462\pi$
$822$	−4.14436e50	−	4.86963e51i	−0.0141177	−	0.165883i
$823$			1.13918e52i			0.379659i	0.981817	+	0.189830i	$0.0607936\pi$
$823$			1.13918e52i			0.379659i	−0.981817	+	0.189830i	$0.939206\pi$
$824$	−3.43827e51	−	1.32059e52i	−0.112112	−	0.430603i
$825$	−3.71306e52			−1.18457
$826$	5.95356e52	−	5.06685e51i	1.85838	−	0.158160i
$827$			4.85397e51i			0.148251i	0.997249	+	0.0741255i	$0.0236165\pi$
$827$			4.85397e51i			0.148251i	−0.997249	+	0.0741255i	$0.976383\pi$
$828$	−1.90823e51	−	1.11297e52i	−0.0570276	−	0.332611i
$829$	3.03027e51			0.0886135			0.0443067	−	0.999018i	$-0.485892\pi$
$829$	3.03027e51			0.0886135			0.0443067	+	0.999018i	$0.485892\pi$
$830$	2.00141e51	+	2.35166e52i	0.0572704	+	0.672928i
$831$			2.98763e52i			0.836581i
$832$	−1.36358e52	+	7.61676e51i	−0.373647	+	0.208713i
$833$	−3.64647e52			−0.977829
$834$	4.03764e52	−	3.43628e51i	1.05959	−	0.0901778i
$835$			1.28534e52i			0.330112i
$836$	−1.13755e52	+	1.95039e51i	−0.285929	+	0.0490239i
$837$	2.84935e52			0.700952
$838$	−7.79631e50	−	9.16067e51i	−0.0187714	−	0.220564i
$839$		−	4.55576e51i		−	0.107361i	−0.998558	−	0.0536804i	$-0.982905\pi$
$839$		−	4.55576e51i		−	0.107361i	0.998558	−	0.0536804i	$-0.0170952\pi$
$840$	1.80316e52	−	4.69469e51i	0.415916	−	0.108288i
$841$	−2.55834e52			−0.577604
$842$	1.19546e52	−	1.01741e51i	0.264191	−	0.0224843i
$843$			3.22367e52i			0.697355i
$844$	−5.93274e50	−	3.46025e51i	−0.0125629	−	0.0732728i
$845$	−1.51120e52			−0.313258
$846$	1.50034e51	+	1.76290e52i	0.0304455	+	0.357735i
$847$		−	1.69800e53i		−	3.37316i
$848$	−5.51070e52	+	1.94690e52i	−1.07172	+	0.378633i
$849$	−6.19370e52			−1.17927
$850$	−3.87919e52	+	3.30143e51i	−0.723103	+	0.0615406i
$851$		−	1.39861e52i		−	0.255249i
$852$	−5.69210e52	+	9.75936e51i	−1.01709	+	0.174385i
$853$	−3.80014e52			−0.664840			−0.332420	−	0.943132i	$-0.607865\pi$
$853$	−3.80014e52			−0.664840			−0.332420	+	0.943132i	$0.607865\pi$
$854$	−2.85928e51	−	3.35966e52i	−0.0489796	−	0.575511i
$855$			1.51750e51i			0.0254530i
$856$	5.36994e51	+	2.06251e52i	0.0881946	+	0.338741i
$857$	−1.39613e52			−0.224528			−0.112264	−	0.993678i	$-0.535810\pi$
$857$	−1.39613e52			−0.224528			−0.112264	+	0.993678i	$0.535810\pi$
$858$	−3.76085e52	+	3.20072e51i	−0.592263	+	0.0504053i
$859$			6.39064e52i			0.985525i	0.870164	+	0.492762i	$0.164013\pi$
$859$			6.39064e52i			0.985525i	−0.870164	+	0.492762i	$0.835987\pi$
$860$	−3.84116e51	−	2.24034e52i	−0.0580084	−	0.338331i
$861$	1.22794e53			1.81602
$862$	3.87342e51	+	4.55128e52i	0.0561002	+	0.659178i
$863$			1.26060e53i			1.78807i	0.447997	+	0.894035i	$0.352138\pi$
$863$			1.26060e53i			1.78807i	−0.447997	+	0.894035i	$0.647862\pi$
$864$	−3.20851e52	−	7.09860e52i	−0.445713	−	0.986110i
$865$	−1.83386e52			−0.249503
$866$	6.24733e52	−	5.31687e51i	0.832477	−	0.0708490i
$867$			1.61678e52i			0.211012i
$868$	−7.32151e52	+	1.25531e52i	−0.935935	+	0.160470i
$869$	2.23552e53			2.79912
$870$	−1.31737e51	−	1.54791e52i	−0.0161570	−	0.189845i
$871$		−	3.01620e52i		−	0.362355i
$872$	1.04568e53	−	2.72253e52i	1.23056	−	0.320388i
$873$	1.13341e52			0.130657
$874$	1.14385e52	−	9.73489e50i	0.129171	−	0.0109932i
$875$		−	9.41707e52i		−	1.04177i
$876$	2.18299e52	+	1.27322e53i	0.236580	+	1.37984i
$877$	−4.36515e52			−0.463454			−0.231727	−	0.972781i	$-0.574438\pi$
$877$	−4.36515e52			−0.463454			−0.231727	+	0.972781i	$0.574438\pi$
$878$	−8.98557e51	−	1.05581e53i	−0.0934640	−	1.09820i
$879$		−	3.82750e52i		−	0.390045i
$880$	2.32472e52	+	6.58013e52i	0.232104	+	0.656971i
$881$	1.95340e53			1.91084			0.955420	−	0.295249i	$-0.0954026\pi$
$881$	1.95340e53			1.91084			0.955420	+	0.295249i	$0.0954026\pi$
$882$	−4.96598e52	+	4.22636e51i	−0.475960	+	0.0405072i
$883$			9.53989e52i			0.895882i	0.894063	+	0.447941i	$0.147843\pi$
$883$			9.53989e52i			0.895882i	−0.894063	+	0.447941i	$0.852157\pi$
$884$	−3.90066e52	+	6.68785e51i	−0.358920	+	0.0615383i
$885$	−4.13664e52			−0.372966
$886$	−1.37707e51	−	1.61806e52i	−0.0121661	−	0.142951i
$887$			1.15695e53i			1.00159i	0.865567	+	0.500793i	$0.166958\pi$
$887$			1.15695e53i			1.00159i	−0.865567	+	0.500793i	$0.833042\pi$
$888$	−7.13788e51	−	2.74154e52i	−0.0605530	−	0.232574i
$889$	−9.14790e52			−0.760484
$890$	−3.35857e52	+	2.85835e51i	−0.273611	+	0.0232860i
$891$		−	9.36627e52i		−	0.747770i
$892$	−3.65088e52	−	2.12936e53i	−0.285647	−	1.66602i
$893$	−1.79870e52			−0.137922
$894$	−7.33300e51	−	8.61628e52i	−0.0551069	−	0.647507i
$895$		−	7.20720e51i		−	0.0530826i
$896$	1.13717e53	+	1.68266e53i	0.820884	+	1.21465i
$897$	3.75428e52			0.265621
$898$	−1.55280e53	+	1.32153e52i	−1.07682	+	0.0916437i
$899$			6.19342e52i			0.420975i
$900$	−5.24464e52	+	8.99216e51i	−0.349422	+	0.0599099i
$901$	−1.48090e53			−0.967118
$902$	3.90006e52	+	4.58258e53i	0.249663	+	2.93354i
$903$		−	1.59852e53i		−	1.00308i
$904$	2.40802e53	−	6.26950e52i	1.48125	−	0.385657i
$905$	−1.04498e53			−0.630137
$906$	−1.70632e53	+	1.45219e52i	−1.00868	+	0.0858450i
$907$		−	4.07057e52i		−	0.235898i	−0.993020	−	0.117949i	$-0.962368\pi$
$907$		−	4.07057e52i		−	0.235898i	0.993020	−	0.117949i	$-0.0376319\pi$
$908$	−2.95166e52	−	1.72154e53i	−0.167695	−	0.978075i
$909$	3.23915e52			0.180419
$910$	−3.73666e51	−	4.39059e52i	−0.0204051	−	0.239760i
$911$		−	2.29061e53i		−	1.22637i	−0.789940	−	0.613184i	$-0.789888\pi$
$911$		−	2.29061e53i		−	1.22637i	0.789940	−	0.613184i	$-0.210112\pi$
$912$	2.19248e52	−	7.74592e51i	0.115088	−	0.0406599i
$913$	−6.21660e53			−3.19948
$914$	6.91543e52	−	5.88546e51i	0.348970	−	0.0296995i
$915$			2.33435e52i			0.115501i
$916$	2.09081e53	−	3.58478e52i	1.01437	−	0.173918i
$917$	1.77544e53			0.844613
$918$	−1.67383e52	−	1.96676e53i	−0.0780807	−	0.917450i
$919$			3.40869e53i			1.55922i	0.626263	+	0.779612i	$0.284584\pi$
$919$			3.40869e53i			1.55922i	−0.626263	+	0.779612i	$0.715416\pi$
$920$	−1.74896e52	−	6.71748e52i	−0.0784512	−	0.301318i
$921$	1.59281e53			0.700631
$922$	1.81216e53	−	1.54226e52i	0.781698	−	0.0665274i
$923$			1.36577e53i			0.577760i
$924$	8.29363e52	+	4.83722e53i	0.344072	+	2.00678i
$925$	−6.59067e52			−0.268151
$926$	−2.88469e52	−	3.38951e53i	−0.115107	−	1.35251i
$927$		−	4.72592e52i		−	0.184948i
$928$	1.54297e53	−	6.97408e52i	0.592234	−	0.267685i
$929$	1.64652e53			0.619845			0.309923	−	0.950762i	$-0.399697\pi$
$929$	1.64652e53			0.619845			0.309923	+	0.950762i	$0.399697\pi$
$930$	5.12424e52	−	4.36105e51i	0.189207	−	0.0161027i
$931$		−	5.06682e52i		−	0.183502i
$932$	4.95254e52	−	8.49135e51i	0.175931	−	0.0301641i
$933$	−3.76541e53			−1.31203
$934$	1.36474e52	+	1.60357e53i	0.0466451	+	0.548081i
$935$			1.76829e53i			0.592850i
$936$	−5.23463e52	+	1.36289e52i	−0.172155	+	0.0448223i
$937$	2.22858e53			0.718978			0.359489	−	0.933149i	$-0.382951\pi$
$937$	2.22858e53			0.718978			0.359489	+	0.933149i	$0.382951\pi$
$938$	−3.90776e53	+	3.32575e52i	−1.23673	+	0.105254i
$939$			4.60569e52i			0.142993i
$940$	1.83792e52	+	1.07196e53i	0.0559792	+	0.326496i
$941$	6.08820e52			0.181918			0.0909590	−	0.995855i	$-0.471007\pi$
$941$	6.08820e52			0.181918			0.0909590	+	0.995855i	$0.471007\pi$
$942$	1.95667e52	+	2.29909e53i	0.0573589	+	0.673968i
$943$		−	4.57457e53i		−	1.31565i
$944$	−1.50194e53	−	4.25125e53i	−0.423797	−	1.19956i
$945$	2.19775e53			0.608423
$946$	5.96554e53	−	5.07705e52i	1.62035	−	0.137902i
$947$		−	2.99009e53i		−	0.796865i	−0.917198	−	0.398432i	$-0.869554\pi$
$947$		−	2.99009e53i		−	0.796865i	0.917198	−	0.398432i	$-0.130446\pi$
$948$	−4.43916e53	+	7.61113e52i	−1.16078	+	0.199021i
$949$	3.05498e53			0.783821
$950$	−4.58738e51	−	5.39017e52i	−0.0115489	−	0.135699i
$951$			3.80937e53i			0.941031i
$952$	1.29657e53	+	4.97991e53i	0.314290	+	1.20714i
$953$	−1.22357e52			−0.0291044			−0.0145522	−	0.999894i	$-0.504632\pi$
$953$	−1.22357e52			−0.0291044			−0.0145522	+	0.999894i	$0.504632\pi$
$954$	−2.01677e53	+	1.71640e52i	−0.470746	+	0.0400634i
$955$		−	2.27826e53i		−	0.521846i
$956$	−3.89829e52	−	2.27366e53i	−0.0876259	−	0.511074i
$957$	4.09190e53			0.902632
$958$	4.97205e51	+	5.84216e52i	0.0107636	+	0.126472i
$959$			1.50283e53i			0.319283i
$960$	−6.85660e52	−	1.22750e53i	−0.142964	−	0.255940i
$961$	2.83648e53			0.580442
$962$	−6.67551e52	+	5.68127e51i	−0.134070	+	0.0114102i
$963$			7.38100e52i			0.145493i
$964$	1.43472e53	−	2.45990e52i	0.277576	−	0.0475916i
$965$	1.46018e53			0.277278
$966$	−4.13957e52	−	4.86400e53i	−0.0771555	−	0.906578i
$967$			3.40345e53i			0.622648i	0.950304	+	0.311324i	$0.100772\pi$
$967$			3.40345e53i			0.622648i	−0.950304	+	0.311324i	$0.899228\pi$
$968$	−1.23996e54	+	3.22837e53i	−2.22665	+	0.579731i
$969$	5.89190e52			0.103855
$970$	6.94219e52	−	5.90824e51i	0.120117	−	0.0102227i
$971$			5.73814e53i			0.974597i	0.873235	+	0.487299i	$0.162018\pi$
$971$			5.73814e53i			0.974597i	−0.873235	+	0.487299i	$0.837982\pi$
$972$	−7.77950e52	−	4.53736e53i	−0.129706	−	0.756502i
$973$	−1.24607e54			−2.03944
$974$	4.66543e52	+	5.48189e53i	0.0749602	+	0.880783i
$975$		−	1.76913e53i		−	0.279046i
$976$	−2.39903e53	+	8.47563e52i	−0.371483	+	0.131243i
$977$	1.42018e53			0.215894			0.107947	−	0.994157i	$-0.465572\pi$
$977$	1.42018e53			0.215894			0.107947	+	0.994157i	$0.465572\pi$
$978$	−3.97759e53	+	3.38518e52i	−0.593637	+	0.0505222i
$979$		−	8.87836e53i		−	1.30090i
$980$	−3.01965e53	+	5.17732e52i	−0.434397	+	0.0744792i
$981$	3.74212e53			0.528538
$982$	−2.03111e52	−	2.38655e53i	−0.0281660	−	0.330951i
$983$		−	9.93520e53i		−	1.35274i	−0.736564	−	0.676368i	$-0.763553\pi$
$983$		−	9.93520e53i		−	1.35274i	0.736564	−	0.676368i	$-0.236447\pi$
$984$	−2.33466e53	−	8.96703e53i	−0.312112	−	1.19877i
$985$	1.49549e53			0.196305
$986$	4.27498e53	−	3.63828e52i	0.550998	−	0.0468934i
$987$			7.64860e53i			0.967995i
$988$	−9.29284e51	−	5.42001e52i	−0.0115484	−	0.0673558i
$989$	−5.95512e53			−0.726703
$990$	2.04950e52	+	2.40816e53i	0.0245592	+	0.288570i
$991$			1.52144e54i			1.79031i	0.445754	+	0.895156i	$0.352936\pi$
$991$			1.52144e54i			1.79031i	−0.445754	+	0.895156i	$0.647064\pi$
$992$	2.30871e53	+	5.10787e53i	0.266784	+	0.590241i
$993$	2.84455e53			0.322795
$994$	1.76948e54	−	1.50594e53i	1.97192	−	0.167823i
$995$		−	1.18272e53i		−	0.129440i
$996$	1.23446e54	−	2.11653e53i	1.32681	−	0.227487i
$997$	−1.38403e54			−1.46095			−0.730473	−	0.682942i	$-0.760700\pi$
$997$	−1.38403e54			−1.46095			−0.730473	+	0.682942i	$0.760700\pi$
$998$	7.38319e51	+	8.67525e52i	0.00765410	+	0.0899358i
$999$		−	3.34149e53i		−	0.340221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.37.b.b.3.15	✓	16
4.3	odd	2	inner	4.37.b.b.3.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.37.b.b.3.15	✓	16	1.1	even	1	trivial
4.37.b.b.3.16	yes	16	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 37 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(261200. - 22229.7i) q^{2} -2.96154e8i q^{3} +(6.77312e10 - 1.16128e10i) q^{4} +1.46296e12 q^{5} +(-6.58343e12 - 7.73554e13i) q^{6} +2.38729e15i q^{7} +(1.74332e16 - 4.53891e15i) q^{8} +6.23874e16 q^{9} +O(q^{10})\)	\(q+(261200. - 22229.7i) q^{2} -2.96154e8i q^{3} +(6.77312e10 - 1.16128e10i) q^{4} +1.46296e12 q^{5} +(-6.58343e12 - 7.73554e13i) q^{6} +2.38729e15i q^{7} +(1.74332e16 - 4.53891e15i) q^{8} +6.23874e16 q^{9} +(3.82125e17 - 3.25212e16i) q^{10} +1.01014e19i q^{11} +(-3.43918e18 - 2.00589e19i) q^{12} -4.81295e19 q^{13} +(5.30689e19 + 6.23561e20i) q^{14} -4.33261e20i q^{15} +(4.45265e21 - 1.57310e21i) q^{16} +1.19657e22 q^{17} +(1.62956e22 - 1.38686e21i) q^{18} +1.66265e22i q^{19} +(9.90879e22 - 1.69891e22i) q^{20} +7.07007e23 q^{21} +(2.24553e23 + 2.63850e24i) q^{22} -2.63389e24i q^{23} +(-1.34422e24 - 5.16292e24i) q^{24} -1.24117e25 q^{25} +(-1.25714e25 + 1.06991e24i) q^{26} -6.29274e25i q^{27} +(2.77232e25 + 1.61694e26i) q^{28} +1.36780e26 q^{29} +(-9.63129e24 - 1.13168e26i) q^{30} +4.52800e26i q^{31} +(1.12806e27 - 5.09874e26i) q^{32} +2.99159e27 q^{33} +(3.12544e27 - 2.65994e26i) q^{34} +3.49251e27i q^{35} +(4.22557e27 - 7.24493e26i) q^{36} +5.31006e27 q^{37} +(3.69602e26 + 4.34283e27i) q^{38} +1.42538e28i q^{39} +(2.55041e28 - 6.64024e27i) q^{40} +1.73682e29 q^{41} +(1.84670e29 - 1.57166e28i) q^{42} -2.26096e29i q^{43} +(1.17306e29 + 6.84183e29i) q^{44} +9.12702e28 q^{45} +(-5.85506e28 - 6.87970e29i) q^{46} +1.08183e30i q^{47} +(-4.65879e29 - 1.31867e30i) q^{48} -3.04744e30 q^{49} +(-3.24192e30 + 2.75908e29i) q^{50} -3.54369e30i q^{51} +(-3.25987e30 + 5.58919e29i) q^{52} -1.23762e31 q^{53} +(-1.39886e30 - 1.64366e31i) q^{54} +1.47780e31i q^{55} +(1.08357e31 + 4.16182e31i) q^{56} +4.92399e30 q^{57} +(3.57270e31 - 3.04059e30i) q^{58} -9.54768e31i q^{59} +(-5.03138e30 - 2.93453e31i) q^{60} -5.38786e31 q^{61} +(1.00656e31 + 1.18271e32i) q^{62} +1.48937e32i q^{63} +(2.83315e32 - 1.58255e32i) q^{64} -7.04115e31 q^{65} +(7.81401e32 - 6.65022e31i) q^{66} +6.26685e32i q^{67} +(8.10450e32 - 1.38955e32i) q^{68} -7.80036e32 q^{69} +(7.76377e31 + 9.12244e32i) q^{70} -2.83770e33i q^{71} +(1.08761e33 - 2.83171e32i) q^{72} -6.34742e33 q^{73} +(1.38699e33 - 1.18041e32i) q^{74} +3.67577e33i q^{75} +(1.93080e32 + 1.12613e33i) q^{76} -2.41151e34 q^{77} +(3.16857e32 + 3.72308e33i) q^{78} -2.21307e34i q^{79} +(6.51405e33 - 2.30138e33i) q^{80} -9.27220e33 q^{81} +(4.53656e34 - 3.86089e33i) q^{82} +6.15416e34i q^{83} +(4.78864e34 - 8.21033e33i) q^{84} +1.75053e34 q^{85} +(-5.02606e33 - 5.90563e34i) q^{86} -4.05081e34i q^{87} +(4.58495e34 + 1.76101e35i) q^{88} -8.78919e34 q^{89} +(2.38398e34 - 2.02891e33i) q^{90} -1.14899e35i q^{91} +(-3.05868e34 - 1.78396e35i) q^{92} +1.34099e35 q^{93} +(2.40488e34 + 2.82573e35i) q^{94} +2.43238e34i q^{95} +(-1.51001e35 - 3.34080e35i) q^{96} +1.81673e35 q^{97} +(-7.95991e35 + 6.77438e34i) q^{98} +6.30203e35i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots - 93\!\cdots\!68 q^{9}+O(q^{10}) \) 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9	\( 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots + 10\!\cdots\!28 q^{98}+O(q^{100}) \) 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9 - 2378142919315561000 * q^10 - 42882825786868930560 * q^12 + 194612014165659174176 * q^13 + 360192888461659120128 * q^14 - 22854023522524990832384 * q^16 + 41803218917907805318176 * q^17 + 138204474036544564333068 * q^18 + 104592026972614096023840 * q^20 - 175281296641396774711296 * q^21 - 4320007363229839528400640 * q^22 + 5118364442017682383085568 * q^24 + 61061610541832160307690800 * q^25 - 70158486911796111631798440 * q^26 - 303534200373547502486016000 * q^28 - 95320519344473743554877152 * q^29 + 361206724962468787334008320 * q^30 + 4662427702586163916855016448 * q^32 - 877278707167997370072668160 * q^33 - 9018225886246079564307746920 * q^34 - 927455191590908629268766192 * q^36 - 30841755082751179145922114784 * q^37 + 78752216997100984306444174080 * q^38 - 138122339194153338361474460800 * q^40 + 99165040763128472781035553312 * q^41 - 193406458925326074258433843200 * q^42 + 303084904999663560614745692160 * q^44 + 1511424637230487714612565241120 * q^45 - 919681205391808405630032112128 * q^46 - 1511312501851283767715389931520 * q^48 - 11342315683204385026834539108848 * q^49 + 11057816114707215621338245966500 * q^50 + 16094442403868561017575461524256 * q^52 + 20911545776251998404629518049056 * q^53 - 42689634574575573966970327785984 * q^54 - 18346492780981997297263940026368 * q^56 - 17591710635767034592583231047680 * q^57 + 33019206317228013320629044602456 * q^58 - 69704584574466315130190074982400 * q^60 + 216576725773383276684585233875232 * q^61 + 406820870675021165265665434183680 * q^62 - 266111502464782094817164314013696 * q^64 - 2065823886943449026422930314993600 * q^65 - 816784109200805225218136599695360 * q^66 + 3502994508232801473127246422490656 * q^68 + 3923547517779842564469076002041856 * q^69 + 312094823977274793710809307489280 * q^70 - 1875458138040165128132392402132032 * q^72 - 13529699358917711874787838251408864 * q^73 + 7683713356825244783786618034273240 * q^74 - 15736875982808342938482824299100160 * q^76 + 22639774155764461736245527294259200 * q^77 - 18389491597233550087389536189698560 * q^78 + 67235988583903584940074904608207360 * q^80 - 40716877106976112078739817594850800 * q^81 + 43227843112149006015980010857549336 * q^82 - 37119022564017857733030089777086464 * q^84 - 206886985961236391219562146270052800 * q^85 + 102108696026625816655543232864792832 * q^86 + 39749581676781586144951142033940480 * q^88 + 461506837768868190077604450557625888 * q^89 - 361659211507857840778210819426233000 * q^90 - 17511543929609412714530045318983680 * q^92 - 231978818535002459544922699145134080 * q^93 - 696830931593880576023589572144120832 * q^94 + 1050073689946737522972596709346639872 * q^96 + 451372245708940284684446048339288096 * q^97 + 1035415270688230597220229005750452428 * q^98

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